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The following is from my notes, and was post by Ray Thornton; it is not proven (not a fact).
My name is Ray Thornton. I am connected to the Quaker Thornton line. This was validated by submitting y-DNA testing and verified through a cousin, Kenneth Jacob Thornton. For several years, I've looked at document over document to verify a father for our William S. Thornton. my 4th great-grandfather.
I see this Needham Matthew Thornton who presumably married a Sarah Sallie Stallworth and had a son named William.
Our best guess, highest probability after excluding all possibilities, is that William's father was Eli Thornton, Sr. I noticed the source below connecting Needham to the Stallworths. However, in all of the databases, I cannot find a "Needham Matthew Thornton".
Eli Thornton, Sr. > William S. Thornton & Jemima Thornton (Butler)
I have found several documents for a Matthew Thornton, Edgefield died 1836/37, wife named Sarah.
They left half of their estate to a William S. Thornton, and the other half to Jemima Thornton Butler.
This Matthew Thornton is in the 1810 and 1820 Censuses for Edgefield.