The 1880 US census, Guadalupe county, Texas indicates your ancestor, [
https://www.wikitree.com/wiki/Williams-39096] Richard Sinclair Williams, and wife, Nancy Jane (Collins) Williams were living in Guadalupe county with their 8 children: Three of the children were born in Alabama, with son, Jonathan born in Texas. Could he be your your Dr John Williams ? Richard had a brother named Thomas also found in the 1880 Guadalupe county, Texas US Census. He had no children named John in his household.
"United States Census, 1880," database with images, FamilySearch (
https://familysearch.org/ark:/61903/1:1:MFNF-2ZD : 15 July 2017), Richard Williams, Precinct 2, Guadalupe, Texas, United States; citing enumeration district ED 73, sheet 248A, NARA microfilm publication T9 (Washington D.C.: National Archives and Records Administration, n.d.), roll 1308; FHL microfilm 1,255,308.