The Bible of William Womack lists two Abner Womacks born in 1799:
Abner C. Womack was born November 24, 1799.
Abner Womack was born February 8, 1799.
The second date, 8 Feb 1799, almost matches the 7 Feb 1799 birth date of Abner C Womack in the Samuel Hand Bible. It was this Abner C Womack who was the son of Abner Womack (10 Feb 1769) and Martha Byars (31 Dec 1774).
So, who was the Abner C Womack born 24 Nov 1799? I am pretty sure it was Abner, son of William Womack and Lucy Womack, who was born in 1799, according to a letter written by his son. It appears that Lucy Womack named a son Abner after her brother, about 10 months after Abner's son Abner was born.