Attribution as a son of Daniel Varvel and Rachel Mitchell is because their daughter Lucinda is living with him in the 1880 census, recorded as sister. (Rachel Varvel is living with Lucinda in 1870, recorded as her mother.)

1860 census of Bath Co., Ky, Owingsville P.O., enumerated 24 July, lists on p. 130 as family #931:
Richd Varvel, 61, farmer; Lucinda, 21; James, 27, farm hand; Clarissa, 5. All born in Kentucky.

Clarissa is James’ daughter by his first wife. Lucinda is presumably James’ sister. Despite the large age difference, Richard is most likely their half-brother, since Daniel Varvel was about 23 years older than Rachel Mitchell, and from the 1820 census almost certainly had a family from a previous marriage.

Mary Jane was raised by Jonathan Jones and his wife Catherine, but considering that they were only 15 and 12 when she was born, it is unlikely she is their daughter. More likely she is a younger sister of one of them.

It is uncertain whether her maiden name was Jones and she was briefly married to a Mitchell sometime before 1860 (when she appears in the census as Mary J. Mitchell, age 17), or if her maiden name is Mitchell and she was misrecorded as Jones in 1850 (when she appears as Mary Jones age 7.)

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 1880 her children Robert and Sarah Varvel are listed with John and Catherine as nephew and niece, but that is not definitive, since quite often great nephew or niece would be listed loosely without the generational qualifier.

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 cannot find this family in the 1870 census.

1880 census of Bath Co., Ky, Sharpsburg precinct, enumerated 8 June, lists on p. 15 as family #124/130:
Varval, James, 48, farm laborer, widowed; Nancy E., 16, dau; Sarah C., 12, dau; Rury (?) A., 10, dau; William, 8, son; Robert, 5, son; Sinda, 34, sister, widowed. All born Ky Ky Ky.

Sarah and Robert are also duplicately recorded in Wyoming precinct, as niece and nephew, with the family of Johnathan and Catherine Jones:

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.