Before March 1, 1656 -- Joseph Fitz Randolph was born at West Barnstable, Barnstable county, Plymouth Colony (now Massachusetts). He was a son of Edward Fitz Randolph and Elizabeth Blossom. 
March 1, 1655/56 Old Style, which means March 1, 1656 New Style. 
August 16, 1670 -- Johannah (Hannah) Conger was born on at Woodbridge, Middlesex County, Province of East Jersey (now New Jersey). She was baptized in 1670 at Woodbridge, Middlesex County, Province of New Jersey. She was a daughter of John Conger and Mary Kelley. John and Mary Kelley Conger were "original settlers of Woodbridge." 
Joseph Fitz Randolph was a New Jersey Patentee of 206 acres of land Piscataway Township. 
January 16, 1687/1688 (i.e., 1688) -- Joseph Fitz Randolph and Johannah (Hannah) Conger married at Woodbridge, Middlesex County, Province of East Jersey (now New Jersey). 
1689 - 1716 -- Joseph and Johannah (Hannah) Conger Fitz Randolph had 12 children (eight daughters and four sons), all born at Piscataway, Middlesex County, New Jersey:
Hannah Fitz Randolph was born on February 4, 1688/1689 (i.e., 1689). In 1725 Hannah Fitz Randolph and Andrew Drake married at ?? She died on June 26, 1742.
Joseph Fitz Randolph Jr was born on February 11, 1690/1691 (i.e., 1691). In 1712 Joseph Fitz Randolph and Rebecca/Rebekah Drake married at ?? He died in 1749/1750.
Mary Fitz Randolph was born on August 3, 1693. In 1712 Mary Fitz Randolph and John Clarkson married at ??
Bethia Fitz Randolph was born on September 20, 1695. In 1714 Bethua Fitz Randolph and John Morris married at ?? She died on September 2, 1757.
Lydia Fitz Randolph was born on January 4, 1697/1698 (i.e., 1698). She died in 1758.
Moses Fitz Randolph was born on April 9, 1700. In 1724 Moses Fitz Randolph and Rachel Hull married at ?? He died on April 7, 1759.
Jonathan Fitz Randolph was born on June 15, 1702. In 1724 Jonathan Fitz Randolph and Margaret Manning married at ??
Susanna Fitz Randolph was born on June 23, 1704. She married a Mr. Merrill.
Ruth Fitz Randolph was born on June 11, 1706. Circa 1725, Ruth Fitz Randolph and Joseph Drake married at ?? She died on September 10, 1776.
Anna Fitz Randolph was born on September 3, 1708. No further record.
Prudence Fitz Randolph was born on November 30, 1712. In 1728 Prudence Fitz Randolph and Captain Nathaniel Manning married at ?? She died on December 1, 1732.
Isaac Fitz Randolph was born on April 21, 1716. No further record.
"Note: some confusion with Mary and Bethia as to which one married John Clarkson and which one married John Morris." 
March 1, 1719/1720 (i.e., 1720) -- date of Joseph Fitz Randolph's will. 
Joseph Fitz Randolph's will cited: Joseph Fitzrandolph of Piscataway, Middlesex County, New Jersey, yeoman, wife Joannah, with all children as listed except Bethia. Son-in-Law John Clarkson was named in the will. Executors were his wife and his son Moses. Witnesses: Thomas Fitz Randolph, Daniel Sutton, Jonathan Borrows.
January 18, 1726/1727 (i.e., 1727) -- date Joseph Fitz Randolph's will was probated. 
June 1726 -- Joseph died at Piscataway, Middlesex county, Province of New Jersey. 
June 26, 1742 -- Johannah (Hannah) Conger Fitz Randolph died at Woodbridge, Middlesex County, Province of New Jersey. 
This surname had many different spellings, including Fitzrandle, Fittsrendolfe, or Fittsrandolfe, with FitzRandolph or Fitz Randolph emerging as the most common. Fitz Randolph is being recommended as the standard, recognizing though that in later years, Fitz sometimes became used as a middle name for sons and optional for daughters. In this Fitz Randolph family, Fitz appears to have been used by all family members as part of their surname: the Oris H.F. Randolph genealogy (referenced below) assumes this to be the case when listing the children in both the family in which Joseph is a child and the one in which he is the father. Variants of the name were used inconsistently in records, including Fitts Randle and Fitzrandolph. The current consensus is to use the surname Fitz Randolph. Please don't hesitate to contact the profile manager if you think this decision should be reviewed!
Need additional original sources for birth, death, marriage, military records. Confirm consistency with census records.
Need to confirm original entry for birth date and transcriptions.
Joseph Fitz Randolph [1656 - 1726]. Find A Grave. Saint James Episcopal Church Cemetery, Edison, Middlesex County, New Jersey. Record added February 19, 2015 by Anonymous. Memorial # 142831742. Accessed by Michael Boynton on January 7, 2015 at 12:25 AM. http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GRid=142831742
Edward Mayes. Genealogy of the Family of Longstreet Completed. Circa 1935. Privately published. Clark T. Thornton, editor. Reprinted 2009. Page 49.
William Montgomery Clemens. American Marriage Records Before 1699. Pompton Lakes, NJ, USA: Biblio Company. 1926. Also available at Ancestry.com. American Marriages Before 1699 [database on-line]. Provo, UT, USA: Ancestry.com Operations Inc, 1997.
Edmund West, comp.. Family Data Collection - Births, Deaths, Individual Records (Source Citation: Birth year: 1655; Birth city: Barnstable; Birth state: MA)
Heritage Consulting. The Millennium File. Salt Lake City, UT, USA: Heritage Consulting.
Ronald V. Jackson. Accelerated Indexing Systems (AIS), compiler. New Jersey Census, 1643 - 1890. Compiled and digitized by Mr. Jackson and AIS from microfilmed schmmedules of the U.S. Federal Decennial Census, territorial/state censuses, and/or census substitutes
Yates Publishing. U.S. and International Marriage Records, 1560 - 1900 [database on-line]. Provo, UT, USA: Ancestry.com Operations Inc. 2004.
Town of Piscataway First Baptist Church. "History of the First Baptist Church of Piscataway with an account of its bi-centennial..." Stelton, NJ: Unknown, 1889. Page 114.
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It may be possible to confirm family relationships with Joseph by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
Y-chromosome DNA test-takers in his direct paternal line on WikiTree: