There are several Branning family trees on Ancestry.com, with some sources.John is said to be the son of William Samuel Branning and Margaret L. Davis; he was one of 8 children of this couple.Both of John's parents were born in Mississippi. William is the son of James Branning (b. 1825, Alabama) and Emily (or Irma) Virginia germany, b. 1824 in Louisiana.
There's a good bit more in the various member trees on Ancestry.