From the Civil War Soldiers & Sailors System at http://www.itd.nps.gov/cwss/soldiers.htm , here are your possible candidates:
Confederate
Rogers, Jackson Confederate Infantry 1st Regiment, Georgia Infantry (State Guards)
Rogers, Jackson Confederate Unidentified Georgia
Rogers, Jackson J. Confederate Infantry 62nd Regiment, North Carolina Infantry
Rodgers, Jackson Confederate Infantry 48th Regiment, Tennessee Infantry (Voorhies')
Rodgers, Jackson Confederate Infantry 40th Battalion, Georgia Infantry
Rodgers, Jackson Confederate Unidentified Georgia
Rodgers, Jackson W. Confederate Infantry 15th Regiment, Mississippi Infantry
Union
Rodgers, Jackson Union Artillery 5th Regiment, United States Colored Heavy Artillery
Rodgers, Jackson Union Cavalry 11th Regiment, Tennessee Cavalry
Rodgers, Jackson J. Union Infantry 17th Regiment, Illinois Infantry
Rogers, Jackson Union Infantry 8th Regiment, United States Colored Infantry
Rogers, Jackson Union Infantry 11th Regiment, United States Colored Infantry (New Organization)
Rogers, Jackson Union Infantry 28th Regiment, United States Colored Infantry
Rogers, Jackson Union Infantry 4th Regiment, Tennessee Infantry
Rogers, Jackson Union Cavalry 11th Regiment, Tennessee Cavalry
Rogers, Jackson Union Infantry 2nd Regiment, Indian Home Guards, Kansas Infantry
Rogers, Jackson Union Artillery 1st Regiment, Ohio Heavy Artillery
Rogers, Jackson Union Infantry 28th Regiment, Illinois Infantry
Rogers, Jackson J. Union Infantry 17th Regiment, Illinois Infantry
Jim Martin