You did not indicate whether the family was black or white.I did find this black family that seems to meet some of the requirements:
1900 Greene County GA
Allen Fordham, 50, May 1850
Victoria, 29, May 1881
Anna 12, Aug 1887
Moses, 10, Feb 1890
Enon (Enoch?), 6, Oct 1893
Elijah, 4, Nov, 1895
Joseph, 3 months, Dec 1899
In 1910, this family appears to be in Dodge County, Jones District:
Allen Fordham, 57
Nimiah, 8 (Maybe this should be Nehemiah -- Bible name)
Living two houses away, as a servant, is Enoch Fordham, age 16.
Also in 1910,
Will Dinkins is living in Jones Distict with his mother, and his sister, Sally
World War I Draft Registration
Enoch Fordham, born Oct 15, 1892 in Greensboro GA
Form states he has a wife and children, but does not list the names.
1870 Wilkinson County
Miles Fordham (age is difficult to read, is 30 or 50)
Julia, (age is 28 or 38)
Clarissa (spelling?), 8
Miles Fordham is in Jones District of Dodge County in 1900, with a son, Homer, born in 1885.
That is all I could find on this particular family group.If this is your family, I hope I have added to your information.