My husband's ancestor, Jonathan Adcock (son of Edward and Tabitha), married Martha "Patsy" Johnson. Martha appears to have been the gr. granddaughter of Littleton Spivey through his daughter Elizabeth's marriage to Benjamin Johnson. I do not have 100% documentation for that, but Martha Johnsonand Jonathan Adcock did name sons Littleton and Spivey--certainly suggestive of a connection.
Two of Martha Johnson's sisters, Sarah and Elizabeth,married Jonathan Adcock's brothers, Stephen and William, respectively.
Jonathan and Stephen Adcock, moved their families to Tennessee about 1820, but William and Elizabeth Johnson Adcock remained in Granville Co., North Carolina.
I believeWilliam and ElizabethAdcock had at least 6 children , including 3 sons, between 1803 and Elizabeth's death about 1817, butI have only been able to confirm two of the sons:
1. Burgess Adcock b. 20 June 1805 in Granville, North Carolina, d. 20 Sep 1884 in Granville Co., North Carolina.Burgess married Catherine Wilkerson on 27 December 1825 in Granville Co., North Carolina
2. Jesse Adcock b. abt. 1809 in Granville Co., North Carolina.Jesse Adcock his first wife shortly before the 1830 census, perhaps in Dickson Co., Tennessee.Jesse married the widow Dolly Mynatt Adcock on 18 Nov 1844 in Dickson Co., Tennessee.
William and Elizabeth had an additional so who was under age 10 on the 1820 census.So, your Littleton Adcock, born 1810/1812, looks like a fit with the family,but I haven't done much more than speculate about the connection.
I do have additional information about William and Elizabeth Johnson Adcock and I will be happy to share.