Signal Abernathy (whom you cite as Tignal) signed his will 4 Apr 1807 in Mecklenburg County, VA. It was probated 11 Jul 1808 in that county and state. In it he names 2nd wife and all of his children. One of whom was Lucy 'Wilkinson', one of whom was Nancy Meredith (deceased).
Nancy's husband's given name and when he died are both unclear in Virginia documentation, but her three children (Lucy, Signal and Aleathean) wound up in Franklin County, GA, with the Elisha & Lucy Wilkinson family.
The Wilkerson surname seem to be interchangeable with Wilkinson. The given name Signal is also sometimes found as Tignal.
This is not my Abernathy line and all I know of Nancy's children is that the boy, Aleathean died young and Signal (or Tignal, if you prefer) and his wife ended up in Mississippi.
It is entirely probable that the Thomas Meredith you find in SC some years earlier was a brother of Nancy's husband, David.