John B. Waits, Franklin's grandfather, has died in 1861 and left an estate legal summary. In there he mentions T. Staton being noted on $75. John B. Waits moved to Smith County, Texas and may not have been aware of T. Staton's early death. I personally do not think he would refer to his daughter Jennifer Teriza as T. Staton. Note T. Staton looking as "Y" but confirmed as "T" in the word "Texas."
Jennifer Teriza Waits is Franklin's mother. She is the daughter of John Bennett Waits (1774-1861) and Mariam Cyempka (1775 - 1817). Jennifer was born in Georgia in 1808 and moved to Lauderdale, Alabama and then Lafayette, Mississippi with her family where she is recorded in both 1850 and 1860 Census. In the 1860 Census she is recorded to live with her 2 children Derril and Caroline next door to her daughter Angeline who married Matthew Lee Taylor (Nancy who married Franklin L. is the sister of Matthew Lee).
Mariam Cyempka, Franklin's grandmother, is believed to have been born in Tennessee and to be a full blooded indian possibly Cherokee, Choctaw or Chipewah. That would make Franklin L. Staton ¼ indian.