According to Samuel Deane, "John Barker was the son of John Barker of Duxbury, and Anna Williams, the daughter of John Williams Sr.'of Scituate (married 1632). John Barker, Sr.' was at Jones's river (now Kingston) 1638. He was drowned, 1652. [He had purchased the ferry (now  Little's Bridge] of John Brewster, son of Elder Brewster, 1641, and was there drowned].
"John Barker, Jr was a sergeant in King Philip's War, and freed from bearing arms at the close of that war, 'on account of wounds received.' He was afterward a Justice of the Peace, and is mentioned as a lawyer in the Colony records in 1674. His brother-in-law, Capt. John Williams, having no children, gave his farm in Scituate, 1694, to Williams Barker, his grand-nephew, son of John, Esq. This is the well known Barker farm north of the Harbour.
" John Barker, Esq. lost his first wife, Desire, 1705, and married Hannah Cushing, (the widow of the Rev. Jeremiah), 1706." 
Children with Desire ANNABLE:
Mary BARKER bc 1677 in Marshfield, married Ensign Otis on 6 Jan 1714.
John b. 4 May 1678.
Desire BARKER b. 22 Sep 1680, Barnstable, d. 12 Jan 1710, Scituate, married Captain Samuel Turner on 20 Nov 1700.
Anne BARKER b. 26 Aug 1682, Barnstable, d. 22 Nov 1682, Barnstable,
Anne BARKER b. 1 Nov 1683, Barnstable, d. before 1729, Scituate, married Robert Thompson on 11 Mar 1714.
John's will is included in full in "Ancestors and Descendants of Captain John Barker (1730-1813)...", by Jerome D Traver referenced. It is sourced as coming from "Plymouth County, Mass: Probates Vol.5:604-612". In it he mentions:
"my beloved wife Sarah Barker"
"my Spanish Indian Maid Servant I have named Mariah"
"my loving son John Barker"
"my loving son Barnabus Barker"
"my loving son Samuel Barker"
"my daughter Mary Otis"
the four "children of my daughter. Desire Turner, deceased"
the four "children of my daughter, Anne Thompson deceased"