Catherine is most likely either a Mitchell or a Varvel, since the children of James Henry Varvel and Mary Jane Mitchell were recorded as nephew and niece in the 1880 census. Also Jonathan was a witness to the consent note for the marriage of John Wesley Varvel and Rosa Ann Bowen.

1850 census of Bath Co., Ky, division 2, enumerated 23 July, lists on p. 13 as family #88:
John J. Jones, 20, farmer; Katharine, 21; Mary, 7. All born in Kentucky.

Considering the ages, it is doubtful that Mary is John’s daughter. More likely she is a sister or niece.

In 1860 I cannot find John/Jonathan (without the family to distinguish him, it would be hard to tell one John Jones of approximate the same age range from another.)

1860 census of Bath Co., Ky, Owingsville P.O., enumerated 9 Aug, lists on pp. 212-213 as family #1541:
David Jones, 43, farmer; Margaret, 33; Mary, 13; Catherine, 34; Mary J. Mitchell, 17. All born in Kentucky.

I believe the Catherine here is Johnathan’s wife, and Mary J. Mitchell is the Mary Jones who was living with them in 1850. I have not determined how they are related to David and/or Margaret Jones, who were both Jones by birth. (Too bad the censuses did not start recording relationships until 1880.)

I cannot find either of them in the 1870 census.

1880 census of Bath Co., Ky, Wyoming precinct, enumerated 16 June, lists on p. 25 as family #221/229:
Jones, Johnathan, 51, laborer; Catherine, 51, wife. Varval, Robt, 5, nephew; Sarah, 11, niece. All born Ky Ky Ky.