I don't think that Jeffrey Jones is the son of John and Susanna (--?--) Jones of Fairfield, Connecticut.
Look at the will of John Jones - it lists six living children: By all accounts, Jeffrey Jones is still living in 1665.
In his will, dated 17 January 1664[/5] and proved 30 June 1665, "John Jones, pastor of the church at Fairfeild," ordered that "seven pounds be taken out of my estate ... & be delivered to the heirs or executors of Captain Cullicke, sometime one of the magistrates in Conecticot jurisdiction being due to him," and "whereas I promised my dear wife Susanna Jones fifty pounds in case I died before her and beside gave her a silver bowl within a little while after that I was married unto her this I do confirm by my last will that these are due unto her, moreover my will is that the said Sussana my wife shall have the use and benefit of my twelve acres of land in the Great Meadows and of my orchard m Fairfeild during her life and after her death that it be divided equally to or amongst my six children John, Ehphalet & my four daughters Sarah Wilso[n] widow, Ruth James. Rebeca Hull & Elizabeth Hill"; "my said wife shall have the remainder of my lot adjoining to the orchard as her own for her and her heirs"; to "my eldest son John Jones pan of my library, to wit the works of Augustin, Chrisostom and of other authors usually called the fathers"; residue "to be equally divided amongst my foresaid six children, John, Eliphaiet. Sarah, Ruth, Rebeca & Elizabeth"; "my wife Susanna Jones [to be] the sole executrix"; "Mr. Gold & Mr. Pell both of Fairfield (to be] the overseers" [Fairfield PR 2:5].
My conclusion is that Jeffrey Jones should be removed from the list of children of John and Susanna Jones.
Tagging Jeffrey Jones to the discussion
That conclusion is congruent with notes from http://genforum.genealogy.com/jones/messages/34782.html