Many sources list this James Jones as the youngest son of Ambrose Jones, but I believe that to be an error. See census notes for details.

James' daughter Catherine's place of birth (born 1818/1819) was given as Bourbon Co., Ky on the birth record of her daughter Lucinda, and his daughter Mary's place of birth (born 1820/1821) was given as Ohio on both the 1850 census and her 1856 marriage record to Mordecai Pearce (although it was given as Ky on the 1860 census), and his son William's place of birth (born ca 1826) was given as Bourbon Co. on the birth records of his children Isaac and Rena.

Bourbon Co. marriage book 2, page 58, records marriage of James W. Jones and Lucinda Brown on 1 Jan 1817. (No bond, no further details.)

James first appears on the tax lists of Bourbon County in 1818, where he is listed with no land, one adult white male, no blacks, one horse. (Those are the only categories.) He is not listed there in 1819 and 1820, which would be consistent with his moving to Ohio (where his daughter Mary was born) during that period. (There is another James Jones appearing with land on Green Creek from 1801 through 1820.)

I haven’t examined the Bourbon County tax lists for 1821-1829.

From a Bourbon County deed book index, James Jones transferred land to Sallie Jones, Book S, p. 189. Book S covers 1825-1829. This would be the time frame that our James Jones moved to Morgan County. He might have been transferring land to his mother. I should get that deed.

1830 census of Morgan Co., KY, lists this family on p.59, line 4:
James Jones, 2 m < 5, 1 m 30-39, 1 f < 5, 2 f 5-9, 1 f 10-14, 1 f 20-29.

These would be James Jr. 2 & William 4, James 30, Lucinda < 1, Sarah 5, Mary 7, Catherine 12, Lucinda 29. Judging by the neighbors, this is the same farm that appears as the household headed by William Jones 70-79 in 1840.

1840 census of Morgan Co., KY, lists this family on p. 317, line 9:
James Jones, 1 m < 5, 1 m 5-9, 2 m 10-14, 2 m 40-49, 1 f < 5, 1 f 5-9, 1 f 10-14, 2 f 15-19, 1 f 20-29, 1 f 30-39.

These would be Josiah 2, David 8, James Jr. 12, William 14, James Sr. 40, unidentified man 40-49, unidentified girl < 5, Nancy 5, Lucinda 10, Sarah 15, Mary 17, Catherine 22, and Lucinda 39.

1850 census of Morgan Co., KY, lists as family #251:
James Jones Sr., 50, KY; Lucinda, 49, VA; Mary, 27, OH; Sarah 25, KY; William, 24, KY; Lucinda, 20, KY; David, 18, KY; Nancy, 15, KY; Josiah, 12, KY; John, 9, KY; Emmy E., 6, KY; William, 86, VA; Sarah, 75, VA; James, 3, KY, Sarah, 1, KY.

This family was listed in the census right after the family of James Jones Jr. (so listed) and wife Emily, so it is almost certain that James Jones Jr. is a son of this James Jones Sr. The youngest James and Sarah are very likely to be grandchildren of James Sr. and his wife Lucinda, but it is not clear who their parents are. The most likely possibility is that this William age 24 is the same listed in the 1860 Rowan Co. census (p. 36, #273) as William Jones, 30; Barbary, 29; James, 13; Sarah A., 12; Rebecca, 10; Mary, 8; Joseph, 6; Isaac, 4; Green B., 6/12; all born in KY. The ages for James and Sarah are about right, and no William & Barbara Jones family (nor any other Jones family with youngsters James and Sarah) appears in the 1850 census of Morgan Co. But that does not explain why Wm would be listed as 30 in 1860 but 24 in 1850, nor where Barbary was in 1850. Note that it is unlikely the age is far off for William (e.g., a mistranscribed 29), because (1) 24 is consistent with the 1830 and 1840 censuses, while an age greater than 25 wouldn't be, and (2) he is listed between his sisters Sarah 25 and Lucinda 20.

1860 census of Rowan Co., KY, (June 11) lists this family on p. 15, #109:
James Jones, 62, VA; Lucy, 59, VA; Emily E., 15, KY. Note that James' state of birth is listed as KY in 1850 and 1870, but as VA in this census.

1870 census of Rowan Co., KY, Pearce prec, p.3/123, lists as family #17:
James Jones, 70, KY; Lucinda, 67, VA.