My Carter family and your Adcocks were intertwined.First, if you look at early t mid 1700's, Spotsylvania Co VA, Joseph Adcock was a neighbor of Joseph and George Carter.Joseph Carter was mentioned frequently with Joseph Adcock (in a number of records), as was Mark Wheeler, who was a first cousin to my Carters.
Then, there was a migration of Baptists to Buckingham from Spotsylvania.The Carters, Wheelers, and some Adcocks migrated as part of Raine Chastain's church.This is outlined in Morgan Edwards "History of the Baptists" book.
Joseph Carter (died 1751 in Spotsylvania) son John went to Buckingham and died there around 1795.In 1798, per the Buck. land tax records, his son John and "John Adcock Jr" owned 51 acres of land through 1803, when "John Adcock Jr." was no longer listed in 1804 as owning part of the land, just John Carter.
This John Carter migrated to Ky around 1811.His son, my g-g-grandfather, was named Joseph Adcock Carter and died mid 1800's, Monroe County Ky.
Clearly the Adcocks and Carters were close, with each using the other's names.
We must share info.I am excited to see a relative of Carter Adcock.