Individual Details

Ann said to be a daughter of Rev. Hezekiah James Balch. There were two Presbyterian ministers of approximately the same age named Hezekiah Balch. It is obvious they have been confused by many researchers. Online research [copies in my files] have revealed the following two Hezekiahs.
[1] Hezekiah Balch [1741-1810], born in MD, established a college and church in Greeneville, Green Co TN, where he died and is buried in the Presbyterian Cemetery. His will listed a wife Anna, probably a 2nd wife, and a son Elijah W. Balch, who was to inherit everything after her death. Online databases list other children but not an Ann.
[2] Hezekiah James Balch [1746-1776] was also born in MD, possibly to James Balch and Anne Goodwin [though there are conflicts here, too]. He was licensed in 1768 and served the Rocky River & Poplar Tent churches in North Carolina. He once visited the Duncan Creek Presbyterian Church in Laurens Co SC which was probably one of the earliest Presbyterian Churches in that state. This Hezekiah married Martha McCandless on 27 Oct 1768 in Harford Co MD. They are usually shown with two children - Ann born about 1771 [Logan Co cemetery book has 1775 for her year of birth] and Hezekiah James Jr, born 1776, and died 1818.

Ann Balch and Samuel Caldwell did name a daughter Martha McCandless Caldwell. They had previously named a daughter Mary Logan Caldwell for the paternal grandmother so likely Martha was named for her maternal grandmother.

Another indication that this is the correct placement of Ann is a lawsuit in Logan Co KY.
Filed 15 May 1845. Equity Box 61, Case #1523. Hezekiah Balch
Suit of Caldwell heirs vs. Caldwell heirs re sale of a slave. [This suit would appear to have been filed a few years after the death of Ann Balch Caldwell in 1842]
The abstract is of necessity incomplete and has perhaps confused some of the parties of similar name. My interpretation that follows is not exactly as found in the Logan Co Wills & Estates abstracts. These papers need to be examined further in the original.
The case states that the party died testate but it's unclear if that was Hezekiah, or when he may have died. Case said "Written 16 Jul 1816" but again it is not clear what was written by whom. The only death that occurred near this time was that of Ann's brother, Hezekiah James Balch, Jr. who died 1818, and it seems to be that man whose will is now being disputed.
Sister, Ann Caldwell, was to receive balance of the estate of Hezekiah J. Balch, and at her death, was to descend to her children. Mother, unnamed, was to get a Negro woman Fan. William E. Parker, friend, received $500 cash; Sarah Parker, friend, to get a feather bed.
Other heirs were:
Mary L. Morgan [Mary Logan Caldwell, daughter of Ann & Samuel, married Abel Morgan and she may have been deceased, see later.]
Robert P. B. Caldwell [son of Ann & Samuel]
Martha Caldwell, widow of Burr [George Burr Jefferson Caldwell, son of Ann & Samuel]
Samuel B. F. Caldwell [the abstract states he is the spouse of the Ann Caldwell, sister, but I believe this in an incorrect assumption. He was their son. The older Samuel had died in 1835 and had no middle initials as far as is known.]
William P. C. Caldwell [son of Ann & Samuel]
Jonathan Keedy & wife Julia Ann Caldwell Keedy [dau of Ann & Samuel]
Heirs of Samuel C. Morgan & Mary L. Morgan are: Oliva E., James C., George B., Robert, Sarah E., & William B. Morgan [Here is a confusion. Mary Logan Caldwell married Abel Morgan according to Logan Co marriage records. Did she have a 2nd marriage to a Samuel Morgan? or have they confused the names of one of her sons as that of her husband?]
Heirs of Burr Caldwell: Joseph A., Henry Clay, Samuel Robert, Maria Julia, George E. Caldwell by their next friends William P. C. Caldwell & Mary Ann [perhaps they are all minors]

The children of Samuel Caldwell & Ann Balch omitted by this record and perhaps deceased without heirs are the following:
Hezekiah James
Martha McCandless, twin of Burr
John J. M. who is said to be buried near his parents, his death date unknown and now unreadable.

Birth	1775
Marriage	6 Apr 1794	Kentucky - Samuel CALDWELL
Death	16 Oct 1842	Logan County, Kentucky

Spouse	Samuel CALDWELL (1771 - 1835)
Child	Mary Logan CALDWELL (1795 - )
Child	Dr. Robert Phillips Balch CALDWELL (1796 - )
Child	Hezekiah James CALDWELL (1799 - )
Child	George Burr Jefferson CALDWELL (1801 - )
Child	Martha McCandless CALDWELL (1801 - )
Child	Samuel Benjamin CALDWELL (1804 - )
Child	John James Madison CALDWELL (1807 - )
Child	William Philpot Curran CALDWELL (1810 - )
Child	Judith Ann CALDWELL (1812 - )