3rd Maryland Artillery, CSA
Alternate Designation
Ritter's Battery

One of the most traveled units in the Civil War, seeing action in Alabama, Georgia, Kentucky, Louisiana, Mississippi and Tennessee, Ritter's Battery was originally organized by Captain John Latrobe, of Baltimore, in the fall of 1861 in Virginia.

Initial training began at Camp Dimmock near Richmond in November.

In December the battery moved to Camp Lee and was mustered into the Confederate Army on January 14, 1862. Term of service: duration of the war. Contingent: originally 92 men. Armament: 2 six-pounder smooth bore, 2 twelve-pounder howitzers and 2 three-inch rifled pieces.

In May, 25 Tennessee recruits joined the battery before it marched as a unit to Clinton Tennessee. In June it was back to Chattanooga, then to Morristown, Loudon and Blain's Cross Roads, where 50 Georgians joined the battery.
http://www.2ndmdinfantryus.org/csart3.html

The American Civil War Research Database in their roster of the Battery, list 285, men and erroneously list all with a September 1, 1861 enlistment date. Thus, this roster is of no help to you.

Thus, the only way of finding your men is walking through the roster at Fold3 which holds some 356 men in their roster of the battery.

I randomly checked through a dozen or so finding only one man enlisting in 1862 while in Tennessee and that being

John O’Hanlon, Private/Artificer, 3rd Battery Maryland Artillery, enlisted July 2, 1862 at Calhoun, Georgia by Capt. Latrob for the war