This Jesse can't be the father of Oliver Clark Kinney b. 1827. Wiki has this info for the Jesse who was the father of the son b. 1827 who was married to Martha Ann Rice.
Oliver Clark Kinney
https://www.wikitree.com/wiki/Kinney-2939
https://www.wikitree.com/wiki/Cox-27266
https://www.wikitree.com/wiki/Kinney-2938
Jesse Kinney
Born 18 Mar 1778 in Rowan County, North Carolinamap
Son of [father unknown] and [mother unknown]
[sibling(s) unknown]
Husband of Sarah (Cox) Kinney — married 3 Feb 1814 in Rowan County, North Carolina
Father of Oliver Clarke Kinney
Died 19 Apr 1857 at age 79 in Habersham County, Georgia
It seems two Jesse Kinneys married wives named Sarah (one Sarah Cox and one Sarah Turner) and both had sons named Oliver Clark Kinney and the info on all of them has gotten confused / co-mingled and incorrect connections are resulting.
It doesn't help that both Jesse Kinneys had wives named Sarah, but there does seem to be a distinction between Sarah Cox and Sarah Turner, if nothing else their dates of brith and death:
https://www.findagrave.com/memorial/36810172/sarah-kinney
This explains why there are parents connected to Oliver Clark Kinney on here who were born just a few shorts years before his 1827 birth. Of course, he coudln't have had a father born in 1822 or a mother born in 1824 as connected here on Geni.