A few thoughts.
Richard-1 Pinkham m. Gylian (---)
John-2 Pinkham m. Martha Otis, daughter of Richard and Rose (Stoughton) Otis.
The best source for this is "Genealogical Dictionary of ME and NH" by Sybil Noyes, Charles Thornton Libby, and Walter Goodwin Davis (Portland, 1939, reprinted Baltimore, 1988), pp. 556-7.
Otis-3 Pinkham m. Abigail Tibbetts, daughter of Ephraim and Rose (Austin) Tibbetts, and a first cousin, once removed, of Otis through the Otis family [Rose Austin was the daughter of Thomas Austin and Anne Otis, she the sister of Martha Otis, above.]
Their marriage record is from Records of Dover Monthly Meeting as reprinted in New Hampshire Genealogical Record (NHGR) 1:51-2 (1903/4).They had five children: Samuel, Anna Rose, Paul and John.The births of the first three are at "Vital Records of Dover, NH 1686-1850" Dover Historical Society (Heritage Books, Bowie, MD, 1990). p. 37.Paul’s birth is at Family Records of the Dover Monthly Meeting as reprinted in NHGR 2:125 (1904/5).This family were Quakers.Otis died on 19 Dec 1763 ("Master Tate's Diary: A Narrative of Events in the town of Somersworth (now Rollinsford) New Hampshire from 1747 to 1778" p. 75) and his estate had an administration in NH State Papers, Vol. 38, p. 4.
There is no primary source record to connect him to Abijah.I don’t believe Abijah was his son.Abijah was not a Quaker first of all.He pops up in Durham and there is no evidence whatsoever on his parents.His family appears in “History of the Town of Durham, New Hampshire (Oyster River Plantation) with Genealogical Notes” by Everett S. Stackpole & Lucien Thompson (2 vols., Rumford Press, Concord, NH, 1913, reprint, Somersworth, NH 1973), pp. 305-6.So the answer is there is no answer.
Now, I have a private theory.Of the nine children of John-2, all were Quakers but two: James-3 and Richard-3.James-3 is my ancestor and he conveniently leaves a will naming all his children and Abijah is not among them.I can also rule out on other grounds Thomas, Otis, Solomon and Amos.That would seem to mean that Abijah must belong somehow to the progeny of Richard-3 Pinkham and his wife Elizabeth Leighton, daughter of Thomas and Elizabeth (Nutter) Pinkham (see: "A Leighton Genealogy: Descendants of Thomas Leighton of Dover, NH" by Perley M. Leighton, 2 vols. (NEHGS, Boston, 1989).
Richard-3, through deeds and birth records, had at least these children: John, Elizabeth, Richard-4, and Tristram.He also probably had a daughter Ann who married William Geddis in 1727.But it seems logical that he could have a son Thomas, named after Elizabeth’s father.A Thomas “Jr.” of Dover, Fisherman is sued on 8 Feb 1734/5 by Elizabeth Allcock of Portsmouth, shopkeeper (NH Provincial Court Cases #10174).In colonial New England Jr. Meant the younger of two men in the same town and does not denote a father/son relationship necessarily.Thomas-3 didn’t have a son Thomas (see below).It is this Thomas (JR.)’s children who are baptised in Dover in 1744.In the Pinkham Genealogy ("Richard Pinkham of Old Dover, New Hampshire and His Descendants East and West" by Rev. Charles Nelson Sinnett (Concord, NH 1908)), these children are given to Thomas-3 as late baptisms.This is not true, because Thomas-3 clearly deeds his lands to his sons Ebenezer, Benjamin and Richard-4 and no other children are mentioned.These baptised children are: Joseph b.c. 1735 who married Elizabeth Deering and then Elizabeth Hayes; Sarah Pinkham and Mary Pinkham.Abijah is not baptised then, but he is the right age (b.c. 1734) to be his son too.Abijah names his eldest son Thomas (very telling).
So, my thought has been that Abijah is the son of Thomas-4 (Richard-3 John 2).Thomas lived with his father Richard who lived to a great age, although Thomas must die shortly after 1744, thus leaving all his children in the care of his father.There’s no proof of this, just circumstancial evidence.
I also posted another message on Abijah which you can find by searching Abijah in the Pinkham forum search box.
Also the History of Durham gives Abijah (Jr.) the wife Sarah Spencer and daughters Margery b. 19 April 1796 m. 24 Oct 1822 Rev. Washington Russell; Abigail b. 13 July 1799, m. 27 April 1820, Joseph Russell of Woodstock, d. 1 Feb. 1890; Pamelia, b. 6 Sept 1805 m. 20 May 1833, Peter Russell of Woodstock, d. 20 July 1877, among other children.
Abijah (Sr.) b. 9 Feb. 1734, d. 3 March 1779, married Rachel Huckins, daughter of Robert and Meribah (Jackson) Huckins on 11 Jan. 1753.Abijah Jr., b. 22 July 1763, married Sarah Spencer on 11 Dec 1783, and he died 8 July 1815.
Let me know your thoughts.