I see him listed on the Mississippi Confederate Grave Registry as being of Company H of the 17th MS Infantry but he is not on that unit's rolls. That registry is on microfilm at the archives in Jackson. I've always been iffy on it's reliability, but sometimes it helps to point you in the right direction.
http://mscgr.homestead.com/MSCGRMap.htmlMartin filed for a pension based on his service, but his application doesn't help very much. He notes that his Captain was named Riley and, as his gravestone indicates, that it was in Ross's Brigade. The only Captain Riley that I could find was a Richard Riley of Company B, 19th MS Infantry. Martin was not in the rolls of that unit.
Have you tried posting a query on the following message board?
http://www.history-sites.com/cgi-bin/bbs62x/mscwmb/webbbs_co...Good luck,
Scott
EDIT:
I see that the 1932 roll for Neshoba County pensioners has Martin under a Captain Foote's company. Note that Company B of the 17th MS was led by a Captain George P. Foote, so perhaps there is some merit to the grave registry noting this company.