Your James A. Martin applied for and was approved to receive a Confederate Pension in Arkansas, there may be some clues to his service noted in his application. These records may be procured here - http://history-sites.com/research/index.html

Arkansas Confederate Pensions
Surname: Martin
Given Name: James
Application Number: 5360
Widow Surname:
Widow Given Name:
Company: G
Regiment: 37
State Served From: Mississippi
Division: Infantry
Pension County: Howard
Death Date:
Application Year: 1901
Widow Death Date:
Comments: approved