His FInd-a-Grave page, which has a lot of personal information from a descendant of his brother Ave Vann, has their parents listed as:
Son of Claw-see & Peggy Vann.
What was the 'white name' for Claw-see Vann?
There is nothing I can find to document John Vann and wife Susannah as Saturday's parents. I'd never heard of Claw-see,so I Googled to see what I could find and this what I found:
https://www.ancestry.com/genealogy/records/james-claw-see-claw-sene...
James "Claw-see" "Claw-sene" Vann
(1780 - 1848)
26 Records:
Born in Cherokee, Georgia, USA on 1780 to Joseph "Joseph David" Vann and Sarah "Sally" Hughes. James "Claw-see" "Claw-sene" Vann married Peggy U TSi Lv and had 8 children. He passed away on 1848 in Cherokee Nation West, Oklahoma.
The link lists their children, which includes Saturday. I realize that's just from someone's personal tree but it does show they have 26 records, whereas the connections here on Geni don't show anything to support the connections as they are here.
While this site doesn't mention Saturday, it has a lot of info about Claw-see:
http://www.pollysgranddaughter.com/2013/01/tracing-back-to-sally-hu...