I am very interested in this family as well. Many Davissons in the United States descend from six of the eight sons of Josiah Davisson (c.1690-1759), of Middlesex county, New Jersey at his death. These six migrated west to Virginia. Two stayed behind, however, John and Nathaniel, and John left issue. John married secondly Charity Christopher, daughter of Jesse & Mercy (Guild) Christopher, and left a son John Davisson, born about 1780 of whom I know nothing more.
I have tripped across J H A Davisson's family often in family research, and met a descendant in Manhattan in 1980 and he gave me a printed family tree of descendants. John Henry Aborn Davisson was born in Trenton in 1838, son of John G A Davisson of Trenton born in 1808. On reviewing the latter's family today, I tried to identify the Hannah Davisson, 72, widowed sister-in-law, who was living with John G Davisson in 1880.
I find Jesse C. Davisson (d. 5 Feb 1865, ae 59) and his wife Hannah (d. 12 Nov 1880, ae 73) in Riverview Cemetery, Trenton. More research is needed, but I wonder if John G A may be the brother of Jesse C ? And I wonder if Jesse C might be named for Jesse Christopher, father of Charity (Christopher) Davisson? Flimsy clues, but I thought they might be worth pursuing.