Children of Jonathan & Abigail (Canfield) Rockwell, all born in Ridgefield include 
Benjamin, b. 5 Jul 1704
John, b. Apr 1705
David, b. 8 Oct 1708
Jonathan, b. 31 Mar 1711
He is buried in Old Town Cemetary, Ridgefield, Fairfield, CT.  It may refer to the Titicus Cemetery in Ridgefield, also known as the Olde Town Graveyard. Below it says he's buried in "Ye Burying Yard" in Ridgefield.
Parents: John Rockwell (1621 - 1673) and Elizabeth Weed Rockwell (1637 - 1676)
Spouse: Abigail Canfield Rockwell (1672 - 1734)
Children: David Rockwell (1708 - 1788)*
Burial: Ye Burying Yard, Ridgefield, Fairfield County, Connecticut, USA
Evidence for the other children has not been located. Did Jonathan or Abigail leave a will, listing children? Did they die young? Did they exist?
No will found for either in Ancestry's will collection
The Barbour Collection of Connecticut Vital Records lists Benjamin, John, David, Jonathan as, using Benjamin as example:
Benjamin, [s. Jonah & Abigail] b. 5 Jul 1704.
Information given in brackets is typically derived from another source.
It is obvious that Jonah and Jonathan are the same person.
David Metcalf: Abigail Rockwell's husband is Jonathan Rockwell, and I found him in the same cemetery as her... notes under his bio about Abigail Canfield Rockwell.
↑ George L. Rockwell. The History of Ridgefield, Connecticut. 1927. Transcribed by Jane Devlin DuhhamWilcox.net Births, Part I
↑ Yates Publishing Publication. U.S. and International Marriage Records, 1560-1900. Online publication - Provo, UT, USA: The Generations Network, Inc., 2004.
James Boughton, comp. A Genealogy of the Families of John Rockwell, of Stamford, Connecticut 1641 and Ralph Keeler of Hartford, Conn., 1639. W.F. Jones. Brooklyn, New York: 1903. Archive.org or GoogleBooks
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It may be possible to confirm family relationships with Jonathan by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
However, there are no known yDNA or mtDNA test-takers in his direct paternal or maternal line.
It is likely that these autosomal DNA test-takers will share DNA with Jonathan:
It says above that Jonathan is the son of John Rockwell and Elizabeth (Weed) Rockwell, yet when I click on "Son of John Rockwell," it gives a John Rockwell who was married to Sarah Ensign and Deliverance (Hayes) Rockwell.