I suspect that Vinson Brannon who married Elizabeth Arterburn in 1800 is either Vinson or Vincent Branham.I assume that Vincent died shortly after this marriage because in 1802 Elizabeth Arterburn married Peter Cornwell b. 1780 Virginia (my great great grandparents).
It is clear that the Branhams intermarried with the Arterburns.See e.g, will of Branham Arteburn dated Apr. 11 1831 Jefferson County, KY To his mother Rachel Arteburn his portion of his father's estate and 287 acres on which testator was living, purchased from Messrs Peay and Parks.At her death, this to go to his brothers, Burris, Jordon, Tarlton, Norborn, Wilia C., and Covington Arterburn. Executor: Brother, Jordon Arterburn. Witnesses: William C. Bullitt, Robert N. Smith.
There was also a will of Daniel Branham Mar. 15, 1810 Jefferson County Kentucky To wife Nancy, for life, land on which she lives with appurtenances and slaves.At her death all of estate to five children, Patsy, Richard, Elijah, Julius, youngest son, and Betsy.Son Elijah to be bound to his uncle Richard Branham until he is of age; Julius to be bound to an honest mechanic until of age, at discretion of executors and his grandfather Richard Bohannon; son Richard to comply with contract made with his uncle George Bohannon.Old negro woman to be provided for. Executors: Isaac Haws, Thomas Sturgeon, George Bohannon. Witnesses: Larkin Bohannon, Jr., Polly Branham, Richard Branham, Robertson Vaughan.
(Daniel Branham married Ann Nancy Bohannon d/o Richard Bohannon).