I found the folowing:
John H. Marshall, a private in Co L, 41st Miss Inf which was from Chickasaw County which borders Monroe Co.
J.G.`Marshall, private, Co. A, 3rd Btn Miss Inf (State Troops) Monroe Co.
J.M. Marshall, private, Co K, 11th Miss Cav (Perrin's) Monroe Co
J. Thomas Marshall, private, Cos A/K 17th Miss Inf Regt, Co A, 17th was from Chickasaw Co.
J.W. Marshall, private, Co F, 2nd Miss State Cav Monroe Co
J.L. Marshal (only one L) private, Co F, 3rd Btn Miss Inf (State Troops) Chickasaw Co.
If you think any of these may be your man, service records can be ordered at th link at top of the page.