Dennis, the Jeff Davis County Cemetery Book does not indicate the unit for Samuel J. Harper.

He is listed in the Bassville City Cemetery as:
Samuel J. Harper
1838 - 1937
[Confederate Soldier, per WPA Records]

This still does not answer your original question as to his unit, perhaps pension and service records can help.

This Gent lived in Covington County until the formation of Jefferson Davis County in 1906.
In the 1930 Jeff Davis County Census, he is listed in the household of Julius C. & Flora (His daughter)Holland.

Mitchell