1860 census of Morgan Co., Ky, West Liberty P.O., enumerated 18 July, lists on p. 76 as household #467:
Conn, Josiah, 33, b. Va, farmer; Hansford, 7, Ky; Caroline, 7, Ky; Perlina, 4, Ky; Henry C., 1, Ky; Nancy J. Webb, 4, Ky; Juliann Conn, 23, Ky.

Julian was apparently listed last just as a correction of an oversight.

1870 census of Elliott Co., Kentucky, Newcombe Fork precinct, lists as family #77:
Conn, Josiah, 44, farmer; Julian, 36; Hanford, 16; Carline, 16 (twins); Perlina, 14; Henry C., 12; Samuel, 10; Minta, 6; Jesse W., 4; Elester (fem), 1. Josiah born in Virginia, all others in Kentucky.

1880 census of Elliott Co., Kentucky, Newfoundland precinct, lists as family #130:
Conn, Josiah, 52, farmer, Va Va Va; Julia A., 43, wife, Ky Ky Ky; Henry C., 20, son, laborer; Jane, dau, 24; Samuel, 19, son, laborer; Minta S., 15, dau; Jessee, 13, son; Helusten (?), 9, son; Francis M., 7, son; Cynthia A., 5, dau; William L., 3, son; Lula, 3/12, dau, b. Feb; Sarah E., 3, granddau. All children born in Ky.
(Josiah’s son Hansford is two households previous at #128.)

1900 census of Elliott Co., Kentucky, Crackers Neck precinct, enumerated 16 June, lists on p. 12B as family #200/205:
Conn, Josiah, 75, b. 1825, Va Va Va, divorced, farmer; Jesse, son, 35, b. 1865, Ky Va Ky, married, Elizabeth, dau-in-law, 23, b. 1867, Ky Ky Ky, married 1 years, mother of 1 child, 1 living; Stella, dau, 5, b. Apr 1895, Ky Ky Ky.

Note that the age and birth year for Elizabeth add up to 1890, not 1900. Also, the number of years married is problematic. It is unlikely that Elizabeth is not Stella’s mother, since she is listed as having 1 living child. It is more likely that the number of years married column was misinterpreted as number of times married. Also her age is consistent with the age of Mary Elizabeth Stephens who married Jesse in 1894.

Morgan County marriage records list Josiah Conn of Russell Co., Va, age 31, born Scott Co., Va, married Juliann Webb of Morgan Co., Ky, born Floyd Co., Ky on Feb 25, 1858.