In the 1850 Covington County Census, there are two Samuel J. Harpers living side by side. One being Samuel Jackson Harper, son of Alexander S., the other Samuel James Harper a brother of Alexander S. Harper.

Samuel James Harper and wife, Catherine E.(Barwick)moved to Simpson County where they are enumerated in the 1860 Census.
He is listed as James S. Harper in this census. This may be the S.J. Harper of Company A, 39th. Regt. and the member of Capt. Barnes Company.

Catherine died in 1868 and by 1870 Samuel James Harper had moved to Winn Parish, LA. His burial site can be found at this site.
http://ftp.rootsweb.com/pub/usgenweb/la/caldwell/cemeteries/adamcem.txt

Although Samuel Jackson Harper is buried in the Bassville City Cemetery, his wife Francis is buried in the Harper Cemetery a few miles away.

From the Jeff Davis County Cemetery Book:

Harper Cemetery
(These are the only marked graves)

Francis M. Harper, wife of S.J. Harper.
19 March 1841 - 23 August 1920

Little Leffie, son of S.J. & F.M. Harper.
31 December 1876 - 10 June 1879

Ella M., wife of B.O. Thompson, and daughter of S.J. & F. M. Harper.
5 February 1866 - 12 September 1889

Catherine E. Barwick, wife of S.J. Harper, Sr.
9 March 1828 - 28 December 1868
Age 40y 9m 19d

A.S. (Alexander) Harper
14 July 1808 - 11 November 1893
Probate Judge, Covington County

Martha Harper, wife of A.S. Harper, daughter of Sam Hathorn
30 June 1807 - 6 June 1882