Jonah Palmer, son of Walter Palmer and his first wife (Unknown), was probably born in England about 1621.  He married first at Rehoboth, 3 May 1655 Elizabeth Grisell.  Jonah married 2nd at Rehoboth, 9 Nov 1692, Abigail (Carpenter) Titus, daughter of William Carpenter, and widow of John Titus. 
Birth: "Jonah, b. say 1621"  This source goes on to say on page 283, that Jonah could have been born anytime in the next years.
He married Elizabeth Grisell 3 May 1655 at Rehoboth, Bristol, Massachusetts.
Jonah and Elizabeth (Grissell) Palmer had seven children: Hannah, Samuel, Jonas, Mary, Elizabeth, Martha, and Grace.
He married, 9 Nov 1692 at Rehoboth, Bristol, Massachusetts, Abigail Carpenter.
"JONAH, b. say 1621; m. (1) Rehoboth 3 May 1655 Elizabeth Grisell (marriage record does not give bride's name [ReVR 276]; on 9 November 1655 "Jonas Palmer and Elizabeth Palmer of Rehoboth" sold to William Bullard, for a consideration part of which was to be paid to "Hannah Grissell daughter of Francis Grissell of Charlestown aforenamed deceased," land in Charlestown "by the last will and testament of the said Francis Grissell deceased given and bequeathed unto the said Elizabeth Palmer" [MLR 1:152-53; Wyman 447]); m. (2) Rehoboth 9 November 1692 Abigail (Carpenter) Titus [ReVR 276], daughter of William Carpenter and widow of John Titus [TAG 70:198-200, 204]. 
Jonah Palmer named all seven of his children in his will, and named some of his daughters by their married names of Grace Carpenter, Hannah French, and Mary Doggett He also named the following grandchildren: Samuel Palmer, son of Samuel, Jonathan and Joseph Titus, Stephen, Lydia and Gershom Carpenter.
Death: 22 Jun 1709, Rehoboth, Bristol County, Massachusetts 
↑Vital records of Rehoboth, 1642-1896, Deaths, page 858
↑ Buys, Doris Palmer, Walter Palmer of Charlestown and Rehoboth, Massachusetts and Stonington, Connecticut: A 400-Year (1585-1985) Family History, published for the author by Historical Publications of Orem, Utah, 1986, pages 91, 88, 1, 40, 44, 47. Cites "research manuscripts of Dr. Byron Smith Palmer". page?
The Great Migration Begins: Immigrants to New England 1620-1633, Volumes I-III. (Online database: AmericanAncestors.org, New England Historic Genealogical Society, 2010), (Originally Published as: New England Historic Genealogical Society. Robert Charles Anderson, The Great Migration Begins: Immigrants to New England 1620-1633, Volumes I-III, 3 vols., 1995). Walter Palmer, page 1379 - 1383
Arnold, James N. Vital records of Rehoboth, 1642-1896. (Providence, Rhode Island: Narragansett Historical Publishing Co., 1897), page 276. Also page 858, Deaths. "PALMER, Jonah, Sr., (died) June 22, 1709."
Ancestry.com Title: Public Member Trees Publication: Name: Ancestry.com Operations Inc; Location: Provo, UT, USA; Date: 2006;Ancestry Family Trees
Personal files of Virginia Basken, Groveland, Massachusetts 01834
Name: Jonas Palmer; Gender: Male; First Marriage Date: 3 May 1655; First Marriage Place: ::Rehoboth; Second Marriage Date: 9 Nov 1692; Death Date: 22 Jun 1709; Death Place: Rehoboth; ::Father: Walter Palmer; Mother: Ann; Spouse: Elizabeth Grissell; Abigail Carpenter; Child: ::Hannah Palmer; Samuel Palmer; Jonas Palmer; Mary Palmer; Elizabeth Palmer; Martha Palmer; Grace Palmer
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It may be possible to confirm family relationships with Jonah 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: