For starters check these listings. Those with the same surnames within the same companies may well be related.
Hopefully, this might narrow your search.

W J. Smith
Edward M. Smith
Alfred M. Smith

Enlisted as Privates
"A" Co. MS 23rd Infantry

..........

W J. Smith
Enlisted as a 2nd Lieutenant

W S. Smith
I B. Smith
N D. Smith
Enlisted as Privates

J W. Smith
Enlisted as a Sergeant

"H" Co. MS 2nd Bn St Troops Cavalry

......

W J. Smith
D Smith
H C. Smith
Isaac Smith
James M. Smith
Enlisted as Privates

Thomas Smith
Enlisted as a Corporal

"A" Co. MS 2nd Bn St Troops Cavalry

Sources used by Historical Data Systems, Inc.:
- Index to Compiled Confederate Military Service Records