just along shot since you have McMullen on surname list

Searching for ancestry of William George McMullen, b 1855. GA.Census of 1880 indicates his mother is Eliza.

1860 census of Clayton County GA includes W G McMullen, 5, with F McMullen, 27, L E, 23, M J, 2 and W A, 7 months, all b GA.
They are in same(or adjacent) household with Benjamin Chapman, 45 and family. Next door is a J A Millner, 44 and family.
Clayton county is adjacent to Henry county.

1880 census of Henry County GA(dated 14 Jun)
Wm McMullin, 23, b GA, parents b GA, farmer
wife, Mary J, 27, b GA, parents b GA
d, Minnie, 4, b GA
s, William W, 3, b GA
s, Andrew J, 1, b GA
mother, Eliza McMullin, 43, b GA, parents b GA, widow

Possible that F McMullen in 1860 could be Felix.
One son of William G McMullen was named Felix.