The following is random research and thoughts put together about the origins of this family. The link from Daniel Fink Sr. to Johann Daniel Finck has not been proven; it is only a supposition. It is based on researching any and all Daniel Fink (Finck) names in Pennsylvania. Here are pieces of information about the likely connection:
Daniel Fink arrived at Philadelphia on the ship Patience, 19 Sept 1749.
Johann Daniel Finck married Maria Agnes Hermann on 13 August 1754 in Philadelphia at St. Michael’s (German Lutheran) and Zion Church. They had three known children baptized at the same church:
Melchior born 30 June 1759, bap. 8 July 1759 Sponsors: Melchior Imdorf and wife Juliana
Johannette Maria born 29 Sept 1762, bap. 13 Oct 1762 Sponsors: the parents and Johanette Maria Schmidt
Daniel born 16 June 1765, bap. 16 June 1765 [believe this to be our Daniel] Sponsors: the parents

Both Peter and Michael Fink were known to have left Philadelphia by 1761 and 1764 respectively as told in History of Lehigh County. Daniel does not show up in any of the tax records for the Northampton area during this period. I presume that means that Daniel stayed in the Philadelphia area with his family. Interestingly enough there are two Finck women married in the same time span at St. Michael's. These could be sisters of our three brother immigrants, especially since one pair appears above as sponsors at a baptism, and Daniel and Agnes appear as witnesses for the other’s marriage. I have noticed that women were not listed on passenger lists. They could have come with one of the brothers.

Melchior Imdorff and Catharin Juliana Finck(in) 10 Nov 1757, witnesses: Gabriel Davis and Christian Cuprian
Michael Bruder and Ilse Finck(in) 30 Sep 1759, witnesses: Danial Pinek [?Finck], Jacob Bruder, and Maria Agnesa Finck(in).

Our Daniel Finck/Fink does not appear in Northampton tax records until 1787 as a single freeman in Lynn Township. He is married by the tax list of 1789. I had presumed marriage in 1788 prior to this. This upholds that premise. I am making a guess that when he came “of age [16]” in 1781 he came to the area and joined the Rangers. He may have been on the frontier or elsewhere until he decided to migrate to the area where his uncles had settled, and he settled in Lynn near “cousins” Peter and Henry. I am unsure of their correct relationship at this time, but I know that this Peter is not the original immigrant as there are two Peters in 1784, one in Salisbury and one in Lynn. The Salisbury one is the immigrant according to Fink family records in History of Lehigh County. Daniel obviously met his wife in Lynn where he also appears in 1790 and 1800 census.
It has been very odd finding all the references to the “three brothers” who came over. There is quite a bit of information on Peter and Michael and where they went and what they did. Daniel is only mentioned as being on the ship. He probably stayed in Philadelphia while the others migrated on, especially in view of the above information. The name Daniel Finck/Fink does not appear very often anywhere, narrowing down the possibilities of where he was.

Using these suppositions I have put together a tentative timeline for the family. All suppositions are in brown text.
1749 PA Peter and Daniel Fink arrive Philadelphia on ship Patience 19 September
1751 PA Michael Fink arrived Philadelphia on ship Janet 7 October
1754 PA Johann Daniel Finck marries Agnesa Hermann 13 August, Philadelphia
1759 PA Melchior Finck born 30 June to Daniel and Agnes Finck, Philadelphia
1762 PA Johannette Maria Finck born 29 September to Daniel and Agnes Finck, Philadelphia
1764 PA Maria Elizabeth Ann Weitzel born March in Lynn Township, Northampton to Jacob and Maria
               Catharine Weitzel (mother deceased, childbirth)
1765 PA Daniel Sr. born (to Daniel and Agnes Finck) 16 May
1781 PA Daniel Sr. serves in Northampton Rangers
1783
1787 PA Daniel Finck, single freeman, pays taxes Lynn Township
1788 PA Daniel Fink pays taxes in Lynn Township
         PA Daniel Sr. and Elizabeth Wetzel married
               Children’s birthdates approximated
1789 PA Daniel Fink pays taxes in Lynn Township
1789 PA Daniel Jr. born
1790 PA Daniel Fink, Lynn Township, census, 1 male 16+, 1 male under 16, 1 female
1791 PA Barbara, daughter of Daniel Sr. born
1793 PA Daniel Finck, Lynn Township pays taxes
1793 PA Jacob, son of Daniel Sr. born
1795 PA Catherine, daughter of Daniel Sr. born
         PA Daniel Finck and wife, Elizabeth, with Martin Weitzel sell Jacob Weitzel land
1800 PA Daniel Finck, Lynn Township census, 2 males under 10, 1 male 26-44; 2 females under 10,
               1 female 26-44
1800 PA Molly, daughter of Daniel Sr. born
1801 PA Susanna, daughter of Daniel Sr. born
1804 PA John, son of Daniel Sr. born
1804 OH Daniel Sr. (and family?) moves to Ohio
         PA Daniel Jr. stays in PA because of apprenticeship, of age??
1804 OH Daniel Sr. buys land from Herman Canfield October
1805 OH Daniel Sr. buys land from Joseph Pangborn
1807 OH Daniel Sr. buys land from Herman Canfield
         OH Daniel Fink Trumbull p. 022 Tax List
1808 OH Daniel Fink Trumbull p. 017 Tax List
1810 OH Daniel Fink Trumbull p. 088 Tax List Canfield
1813 PA  Daniel Jr. and Mary Susannah Kantner married
1814 OH Barbara Fink and Mathias Boyer married
         PA Absolom Fink, son of Daniel Jr. born 2 September
1816 PA John Fink, son of Daniel Jr. born
1817        Daniel Fink Jr. moves with family to OH
1818 OH Daniel Fink III born 25 April, Canfield
1819 OH Martin Fink, son of Daniel Jr., born
1820 OH Daniel Fink (Sr.) Trumbull p. 237 Census Canfield
                Daniel Fink (Jr.) Columbiana p. 026 Census Beaver
1821 OH Daniel Fink buys land from William Treat
1823 OH Daniel Fink lease mill from Fleurwelling
1824 OH Daniel Fink buys land from William Treat
         OH George Fink, son of Daniel Jr. born
1825 OH Anna Maria Fink, daughter of Daniel Jr. born
1829 OH Elizabeth (Weitzel) Fink dies, 15 Aug
1830 OH Daniel Fink Trumbull p. 099 Census Brookfield 1 male under 10, 2 males 5-10,
                2 males 10-15, 1 male 15-20, 1 male 40-50; 1 female under 5, 1 female 40-50
         OH Mathias Boyers 1 male 5-10, 1 male 10-15, 1 male 40-50, 1 male 60-70
                (Could be Daniel Fink living with daughter Barbara); 1 female 10-15, 1 female 30-40
         OH Henry Fink, son of Daniel Jr., born, 22 July
1833 OH Mary Susannah, daughter of Daniel Jr. born
         OH Daniel Jr. dies (possible from Emma letter)
1834 OH Daniel Fink, Sr. buys land from Mathias Boyer (given to Molly in will)
1836 PA Absolom Fink marries Mary Ann Chapman Mercer County, PA 10 July
         OH Daniel Sr. dies August
1840 OH Martin Fink marries Polly Weaver, 16 July, Trumbull County
1843 OH John Fink marries Maria Brobst 18 Jan Trumbull County
1846 OH Daniel III marries Elizabeth Little 27 Aug, Canfield
1849 CA George Fink leaves for California
         OH Anna Marie Fink marries Hiram Johnson 6 August, Canfield
1850 OH Henry Fink marries Susan Summer 17 November 1850, Canfield
1854 OH Henry Fink dies 3 March, leaving wife and 2 children
1856 OH Mary Susannah Fink marries Samuel Detrick 30 December 1856, Canfield
1875 OH Mary Susannah (Kantner) Fink dies 10 April, Canfield
©2012-2020 Original narrative and timeline by Nancy Ratay

1790 Pennsylvania, Northampton County, Lynn Township, page 175, film M637-08
Daniel Finck 1 male over 16 years of age, 1 male under 16 years, 1 female

1800 Pennsylvania, Northampton county, Lynn Township
Daniel Finck 2 males under 10, 1 male 26-44; 2 females under 10, 1 female 26-44, page 567, film M32-37

1810 No Ohio Census Data

1820 Ohio, Trumbull County, Canfield Township, page 596, film M33-89
Daniel Fink (Sr.) 1 male 10-15, 1 male 16-25, 1 male over 45; 1 female 10-15, 1 female 16-26, 1 female over 451479

1830 Ohio, Trumbull County, Canfield Township
Mathias Boyers 1 male 5-10, 1 male 10-15, 1 male 40-50, 1 male 60-70 (Could be Daniel Fink living with daughter Barbara); 1 female 10-15, 1 female 30-40

----------------------------deceased

Daniel served in the Revolutionary War with the Northhampton Co. Rangers of Pennsylvania. He received a pension.

Volume 8 1836 June Term p 398
Daniel Fink Dec’d
I Daniel Fink of the township of Canfield and of the County of Trumbull and in the State of Ohio do make and publish this my last Will and Testament in manner and form following that is to say. First it is my will that my funeral expenses and all my just debts be fully paid Second I give and devise to my eludes [sic] son Daniel Fink Juner deceased or to his heirs the full sum of fifty dollars in cash, Third I give and devise to my eldest dother [sic] Barbra Boyer the full sum of one dollar in cash; fourth I give and devise to my second son Jacob Fink the full sum of fifty dollars in cash. Fifth I give and devise to my second dothers [sic] son Daniel Shafer the full same of fifty dollars in cash Sixt [sic] I give and devise to my third Dother [sic] Malley Fink the ten acre Lot wich [sic] was deed to me by Mathias Boyer the Executors is to give a good warrantee deed to the said Molley Fink for said ten acres of land above named. Seventh I give and devise to my fourth dothers dother [sic] Susan Fillnogel the full sum of fifty dollars in cash Ninth it is my Will that the Executors is to sell all the real and personal property except the ten acres above named the Executors is to spend one hundred and fifty dollars spend in Law with my Dother [sic] Barbra Boyer about the title of land if the Executor sees fit the remainder part is to be divided in equal partes [sic] excepting Barbara Boyer is not to have anything more than the one dollar before named And lasty [sic] I hereby constitute and appoint my son Jacob Fink to be the Executor for this my last Will and Testament revoking and annulling all former Wills and Testament [scored through] in testimony whereof I have here unto set my hand and seal this the 16 day of [set my hand and seal this of - crossed out] May 1836
Daniel X Fink
[his mark]
Signed published and declared
by this above name (X his mark) Daniel Fink
as and for his last Will and
Testament - in presents of us who at his request have signed as witness to the same
Adam Lynn
Josiah Wood
Rec’d August 24, 1836 recorded by George Parsons Clerk

Volume 8 1836 June Term p 425
Daniel Fink Dec’d
This day the last Will and Testament of Daniel Fink late of Canfield deceased was produced in court and proved by the oaths of Adam Linn and Josiah Wood and approved by the Court - thereupon Jacob Fink the Executor named in the Will appeared in Court and took the oath required by Law.

Ordered that he be give bond with surety in the penal sum of Four thousand dollars. Adam Lynn & John R Church are accepted as his sureties and Jonathon Kline, Henry Tubb [?] & Peter Lynn are appointed appraisers of personal property

Volume 8 1836 November Term p 456
Daniel Fink Dec’d
The State of Ohio
Trumbull County of}
Before me Adam Lynn a justice of the peace in and for said County. Personally came Peter Lynn Jonathon Cline Henry Chup appraisars [sic] os the estate of Daniel Fink late of Canfield township in said County Deceased. And were sworn well and truly to appraise all the Goods and chattles [sic] of said Estate which shall be presented to them for appraisment. Given under my hand this the 24th 1836. September 24th 1836. Adam Lynn Justice of the peace

Inventory
A true and accurate inventory of the Goods and chattles of Daniel Fink late of the township Canfield in the County of Trumbull Deceased as presented to the undersigned Peter Lynn Jonathon Cline and Henry Chup appraisars [sic] appointed by the court of common pleas of said County by Jacob Fink administrator of said Estate of this the 24th day of September AD 1836

To one lot in Canfield to contain Eighty Acres valued at $13 per acre 1000.00
In Johnston township 4 Lost undivided in Lot No 106 one 8 part of 15 acres is A17/8 2.50
In lot No 49 one 8 part of 14 Disct is A16/8 4.00
In lot No 14 one 8 part of 170 Dito 212/8 30.00
In lot No 10 P13 [?] one 8 part of 40 Ditto 5 2.50
One red cow 15.00
One red heifer 8.00
One old cooking stove 10.00
On half barrel of Sold [?] 1.50
15 Tow Lynens 2.70
4 chairs 1.00
One teapot 1.00
1 Tin pail and 5 Glass Bottles .50
1 Stand .25
3 Ironpots 1.00
9 Milk crocks 1.00
1 Old ax .50
1 Pair tongs and shufels .50
2 Pad [sic] dishes .25
1 Old chain .37
1 Coffee mill .25
1 candlestick .18
2 pair of brods [?] .50
1 Cake of Beeswax .75
1 Looking glass .12
1 Watch 1.50
1 Old hopel [?] .37
1 Peace of soleder .12
2 Tun of hay 7.00
Total amount of appraisment $1093.36

Given under our hands this the 24th 1836
Jonathon Kline
Peter Lynn
Henry X Chup [his mark] Appraisars
Filed Nov 24. 1836

Sale List
List of the sales of the Goods and chattels belonging to the Estate of Daniel Fink late of Canfield township of Trumbull County deceased sold at public vendue by the undersigned Administrators of said Estate on the 15 day of October A.D. 1836
Purchasers named Property Price
Jonathon Cline 80 acres of Land in Canfield 1112.00
Sarah Wetmore To one 8 part of fifteen acres 4.50
Walter Jonston To one 8 part of 14 acres 4.22
Dito To one 8 part of 170 acres 39.92
Dito To one 8 part of 40 acres 2.50
Michel Sowers To one Red Cow 20.00
Dito One old Kuking stove 18.00
Dito One cidel [?] 2.58
John Naff To one red heifer 12.01
Prins Way To one barrel of salt 4.10
John B. Butt One watch 2.76
Mathias Barger To 15 yards tow linen 1.70
Dito One Table 1.00
Henry Ruberight 4 chairs 1.00
Dito To pail & botel .75
Dito To 3 Iron pots 1.00
Dito To 2 bedsteads .44
John Boyer To mitte crocks .75
John Boyer To 1 pare of tungs & shovel .50
Dito To 2 Puder dishes .25
Ditto To 1 Old chain 1.50
Charles Buggets [?] To 1 Coffee mill .25
Ditto To 1 candlestick .18
Ditto To 2 Pare of boods 2.47
Daniel Warer To 1 Tun of hay 4.25
Ditto To one Sugar Glass .25
Jacob Fink Bot sundry articles 3.47
Molly Fink “ 3.47
Total amount of sale 1238.83
Given by me Jacob X Fink, Administrator (His mark)
Filed Nov 24, 1836

Volume 9 1838 March Term p156
Daniel Fink Deceased
This day the Executor on the Estate of Daniel Fink deceased filed a final settlement Ordered that the same remain on file until the next Term for exceptions etc.

Volume 1841 March Term p 41
Daniel Fink Dec’d
Final Settlement
Jacob Fink Executor of the estate of Daniel Fink deceased in account with said estate.
This accountant charges himself as follows. At a partial settlement the Court found in my hands one thousand five hundred and sixty one dollars & fifty cents. Total $1561.50
p42
This accountant claims the following heirs of the estate of Daniel Fink deceased in full of their Legacies as follows to wit,
John Fink 260.25 (son)
Michael Sowers & Catharine Sowers 200.25 (daughter & husband)
Mary S. Fink 195.61 (widow of first son)
Daniel Shaver 50.00 (grandson through Catharine)
Molly Fink 260.25 (daughter)
Absolom Fink 32.32 (grandson through deceased son Daniel)
John Fink Jr. 32.32 (grandson through deceased son Daniel)
Solomon Crouse Guardian 260.25 (guardian for Susan, granddaughter through Susanna Fillnogle)
Jacob Fink 260.25 (second son)
[Total] $1561.50
Jacob Fink Executor of the estate of Daniel Fink deceased
————————————————————————
The following information is from: Abstracts of Probate Records,
Trumbull County, Ohio 1803-1843
Published by the Trumbull County Chapter of O.G.S., 1986 Whipporwill Publications, page 62
FINK, Daniel, late of Canfield
Will: Debts to be paid. to eldest son Daniel FINK Jr. deceased, to his heirs $50; to eldest daughter Barbra BOYER $1; to 2nd son Jacob $50.; to 2nd daughter's son, Daniel SHAFER $50; to 3rd daughter Malley/Molly FINK the 10 acre lot deeded to me by Mathias BOYER. To my 4th daughter's daughter Susan FILLNOGLE/VELNAGLE $50; Executors to sell real estate and personal property except 10 acres and to spend $150 in law with daughter Barbra BOYER about the title of land if executor sees fit. Remainder to be divided in equal parts except that Barbra BOYER is not to have anything more than the $1 before named.
Executor - Jacob FINK; 16 May 1836, Daniel (his mark) FINK
Witnesses - Adam Lynn, Josiah Wood
Rec'd 24 Aug 1836 (vol. 8-page 398) June 1836,
Will proved by Adam Linn/Lynn, Josiah Wood; Executor Jacob FINK; Bond $4000; Sureties Adam Lynn, John R. Church. Appraisers Jonathan Kline, Henry Iubb? And Peter Lynn (vol. 8-page 425)
24 Aug 1836 - Special Court. Inventory filed 24 Sep 1836, sale 15 Oct 1836. Debts due the estate (vol. 8-page456). Partial settlement filed
(vol. 9-page156) Mar 1838. Rec'd $1473.92; paid $293.42. Balance unaccounted for. No heirs named as such. Final settlement filed by executor Oct. 1840. Final settlement details by Jacob FINK executor in full of their legacies - John FINK $260.25. Michael & Catharine SOWERS
$200.25. Mary S. FINK $195.61. Daniel SHAFER/SHAVER $50. Molly FINK $260.25. Absalom FINK $32.32. John FINK Sr. $32.32. Solomon CROUSE, Gdn. $260.25. Jacob FINK $260.25, (vol. 11-page 41) Mar. 1841.

FINK, Daniel Jr. late of Canfield
this note added by Mitzi Fenstermaker, who was the editor of this volume: "see DAR Roster - Daniel, Sr. married Elizabeth Ann WELZEL/WELTZEL; Daniel Jr. married Susan KENTNEY, father's will stated Daniel Jr. deceased."
Mary Susannah FINK appointed gdn to MORDIN, Daniel & George FINK until 21; to Henry FINK until 14; to Anna Maria until 18; to Mary Susan until 12; children of Daniel, Jr.