I don't think Alabama was recording births in 1849 when William was born. You can look that up.
I'd look in Fayette Co. AL genealogical and historical societies for church, baptism records to prove that William was John and Sarah's child.
To "prove" that John was his father, look for John's probate records. I see on your tree that he died in 1878 in Yalobusha Co. MS.
However to make things more confusing, there was another William Whitson in 1860 in Tuscaloosa, Tuscaloosa, AL.
John and Sarah's family continued to live in Fayette Co. AL through the 1860 Census.
1870 Fayette Co. AL
William Whitson, b. AL, 21, farmer
Sarah, b. AL, 15
I assume that Sarah died before the 1880 Census.
1880 Calhoun CO. MS
Wm Whitson, b. AL, 32, farmer
Octavia, b. MS, 23
Littleton E., son, b. MS, 5/12ths
That's the last place I find William and Octavia. However their son Jess was born Aug 24, 1888, Calhoon Co. MS and their daughter Sarah Frances b. 1891 in Yalobusha Co. MS. I assume they both died in yalobusha County.
Mississippi wasn't recording deaths prior to 1912.
You can find a lot of cemetery inventories anc church records at Mississippi State Library, http://lib.msstate.edu/specialcollections/collections/geneal...
I'd also contact the Yalobusha Historical Society, www.facebook.com/
and ask if they have a local death index, indexed newspaper death notices and cemetery inventories. William's parents names might be in his death notice.
Jess Whitson died Oct 3, 1963 in Potter Co. TX. I'd contact the local genealogical and historical societies and order a copy/scan of his obit.
Sarah married William Chaney and died in 1960 in Sharkey Co., MS.
I'd contact the Sharkey-Issaquena County Library, www.facebook.com/
and ask about a scan/copy of her obituary. Successful Searching!