SEPT 5, 2021-- NOTE FROM MEMORIAL MANAGER:
THERE ARE DISCREPANCIES REGARDING THE CHILDREN OF SAMUEL AND ELIZABETH. IF ANYONE HAS DOCUMENTATION VERIFYING PERSONS OR DATES, PLEASE SUBMIT AN EDIT AND INCLUDE THE DOCUMENTATION. THERE ARE MANY ERRORS IN ANCESTRY AND FIND-A-GRAVE PERTAINING TO THIS LINE, AND THEY KEEP BEING PERPETUATED. THANK YOU!
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The following is taken from a posting on Ancestry.com:
https://www.ancestry.com/boards/surnames.fitzrandolph/201
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This is a public service announcement for anyone related to SAMUEL FITZ RANDOLPH (RANDOLPH), son of NATHANIEL FITZ RANDOLPH and REBECCA MERSHON:

I have been finding many discrepancies on multiple platforms regarding dates and locations for Samuel, son of Nathaniel. The correct information below. If anyone has conflicting info, please contact with me and include documentation.

SAMUEL FITZRANDOLPH, son of NATHANIEL FITZRANDOLPH and REBECCA MERSHON, was born May 2 1741 in Princeton, N.J (1,3,5,6). He married AMEY EDWARDS Mar 6 1762 in NJ.: https://familysearch.org/ark:/61903/1:1:FC7M-PPD (1,2,3,5,6,8) (date listed is the date the license was given. They were married on the 6th)

They had 5 known children as recorded in Nathaniel's "Book of Records" held at Princeton University (3):
1. Joseph b. Mar 26 1763 in So. Brunswick, NJ (3,5,6)
2. Hannah b. Apr 15, 1765 (3,5,6)**My great grandmother. She married Ezra Phillips in Greene Co, TN Sept 15 1787 and died in Pine Swamp, NC on July 7 1839 (4)
3. Samuel b. Sept 27 1767 in So. Brunswich, NJ died in NC3,5,6
4. Mary b. Aug 21770 at Atkins River, N.C.(3,5,6)
5. Daniel b. Dec 16 1772 in North Carolina, d. Mar 23 1773 (3,5,6)

He married an Elizabeth______ sometime between 1773-1778, after the death of Amy, and before the birth of Nancy.(5)
These are the probable children of Samuel and Elizabeth:(5)
1. WILLIAM RANDOLPH was born in 1797 in Buncombe Co. NC. Died in 1870.(5)
2. SARAH B. RANDOLPH was born in 1798 in Buncombe Co. NC. (5)
3. THOMAS RANDOLPH was born 1805 in Buncombe Co. NC. Thomas married KEZIAH PHILLIPS. (5)
4. RACHAL RANDOLPH was born circa 1800 - 1810.(5)
5. BECKY RANDOLPH was born circa 1800 - 1810. (5)
Other probable children of Samuel Randolph are:
1. NANCY RANDOLPH was born 9 Nov 1778 in NC or TN. She married JONATHAN PHILLIPS in Haywood County, NC. She was mentioned in the Will of Samuel (5)
2. JAMES RANDOLPH was born either in the 1780's or the 1790's in NC or TN.(5)

ALSO, the Samuel who is the son of Nathaniel and Rebecca died in abt 1816 in Jack's Creek, NC. His will was dated 22 Jan 1816. (5)

The confusion comes from that fact that there were several Samuel Fitzrandolphs born around the same time frame. So, I'm going to show all of them together below, starting with their lines traced back to Edward Fitzrandolph and Elizabeth Blossom.

1. EDWARD FITZRANDOLPH/EIZABETH BLOSSOM-BENJAMIN FITZRANDOLPH/SARAH DENNIS-NATHANIEL FITZRANDOLPH/REBECCA MERSHON-SAMUEL FITZRANDOLPH
Samuel Fitzrandolph, son of Nathaniel Fitzrandolph and Rebecca Mershon. Born Princeton, NJ May 2 1741 (1,3,5,6). Married Amey Edwards Mar 6 1762 in N.J. (2,3,5,6) At some point before his daughter Hannah was married in 1787, he had dropped the 'Fitz' from his name, as he appeared as a bondsman on her marriage document as Samuel Randolph (4). He married Elizabeth Margaret Jackson (?) in N.C sometime after 1773.(5) Died in Jack's Creek, N.C. Abt 1815/1816. Will was proven Jan 1816(5)

2. EDWARD FITZRANDOLPH/ELIZABETH BLOSSOM-THOMAS FITZRANDOLPH/ELIZABETH MANNING-JONATHON FITZRANDOLPH/MARY BONHAM-SAMUEL FITZRANDOLPH
Samuel Fitzrandolph, son of Jonathon Fitzrandolph and Mary Bonham. This Samuel was born in Piscataway, NJ in Oct 1738 and died in New Salem, WV (VA) Feb 25 1825 (6,7,10) He married MARGARET FITZRANDOLPH Mar 26 1721 (6,7, 9,10). He was an Ensign in Capt. Wm. Johnson's Company, 2nd Regiment, Sussex Co, NJ. (Rev War) (6,7,10).

3.EDWARD FITZRANDOLPH/ELIZABETH BLOSSOM- NATHANIEL FITZRANDOLPH/MARY HOLLEY-SAMUEL FITZRANDOLPH
Samuel Fitzrandolph, son of Nathaniel Fitzrandolph and Mary Holley, was born 1668 in Barnstable, MA.(6,8) He married MARY JONES June 8 1693 in Woodbridge, NJ.(6,8,11) He died June 25, 1754 in Woodbridge, NJ (will was proved May 22, 1750; written as Samuel Fitzrandolph Sr.). (6,8,12)

4. EDWARD FITZRANDOLPH/ELIZABETH BLOSSOM- NATHANIEL FITZRANDOLPH/MARY HOLLEY-SAMUEL FITZRANDOLPH/MARY JONES-SAMUEL FITZRANDOLPH
Samuel Fitzrandolph, son of Samuel Fitzrandolph and Mary Jones, was born Dec 16, 1694 in Woodbridge, NJ (6,8). He first married FRANCIS (____) on Nov 25, 1719.(6) He then married JOHANNAH KINSEY in 1728.(6,8,13)

I hope this clears things up for everyone. I was very confused myself at first researching this years ago. However, comparing the documentation and getting a hold of "The Descendants of Edward Fitz Randolph and Elizabeth Blossom 1630-1950" really cleared things up.

References:
1. Ancestry.com. New Jersey, Births and Christenings Index, 1660-1931 [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2011.
2."Massachusetts, Marriages, 1695-1910," index, FamilySearch (https://familysearch.org/pal:/MM9.1.1/FC7M-PPD : accessed 9 December 2014), Samuel Randolph and Amy Edwards, 05 Mar 1762; citing reference ; FHL microfilm .
3. Nathaniel Fitz Randolph "The Book of Records", an unpublished genealogy manuscript owned by Princeton University. Princeton University owns all rights to this material. It may not be published in any form without their express permission.
4. Friel, Shirley Phillips. The Phillips Family, Our History, Our Heritage. Angola, Ind. (1104 Crestview Dr., Angola 43703): S.P. Friel, 1988. Print.
5.http://archiver.rootsweb.ancestry.com/th/read/RANDOLPH/2010-05/1273680326
6. Christian, Louise Aymar, and Howard Stelle Fitz Randolph. The Descendants of Edward Fitz Randolph and Elizabeth Blossom 1630-1950. 1950. Print.
7. Ancestry.com. U.S., Sons of the American Revolution Membership Applications, 1889-1970 [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2011.
8. Hornor, William S. This Old Monmouth of Ours: History, Tradition, Biography, Genealogy, and Other Anecdotes Related to Monmouth County, New Jersey. Baltimore, Md.?: Clearfield, 1999. Print.
9. U.S. and International Marriage Records, 1560-1900. Source number: 703.003; Source type: Pedigree chart; Number of Pages: 3.
10. Randolph, Corliss Fitz. A History of the Seventh Day Baptists in West Virginia including the Woodbridgetown and Salemville Churches in Pennsylvania and the Shrewsbury Church in New Jersey;. Plainfield, N.J.: Printed for the Author by the American Sabbath Tract Society, 1905. Print.
11. Ancestry.com. American Marriages Before 1699 [database on-line]. Provo, UT, USA: Ancestry.com Operations Inc, 1997.
12. Ancestry.com. New Jersey, Abstract of Wills, 1670-1817 [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2011.
13. Swarthmore College; Swarthmore, Pennsylvania; Quaker Meeting Records; Call Number: MR Ph:547.