Census files and other researchers have your John T Y as son of John Yarbrough 1800 Chester/Fairfield SC and wife Elizabeth.
Name: John Yarborough Age: 50 Estimated birth year: abt 1800 Birth Place: South Carolina Gender: Male Home in 1850Fairfield, South Carolina Family Number: 303 Household Members: Name Age John Yarborough 50 Elizabeth Yarborough 46 William Yarborough 15 John T Yarborough 10 Elizabeth Yarborough 2 Jason Yarborough 15 (Nephew, son of Peter S Y) Source Citation: Year: 1850; Census Place:, Fairfield, South Carolina; RollM432_852; Page: 220B; Image: 445.
Name: John Yarborough Age in 1860: 20 Birth Year: abt 1840 Home in 1860: Fairfield, Fairfield, South Carolina Gender: Male Post Office: Winnsboro Value of real estate: View image Household Members: Name Age Tarlton Murphy 68 John Yarborough 20 Nancy Yarborough 22 (John's sister) Source Citation: Year: 1860; Census Place: Fairfield, Fairfield, South Carolina; RollM653_1219; Page: 260; Image: 525; Family History Library Film: 805219
Research shows that John Y b 1800 is the son of Asa Y 1770 NC-1840 AL and Sarah Jane White 1780- aft 1840 AL.
Another researcher of your line has Lucinda H. Gilmmer as a Gilmore. Possible parents were John Gilmore 1808 NC-1871 AL and Temperance Dean.
This is not my line. Ann Broadbent gave the best advice - obtain a death certificate.