Gibson's Battery, also known as Company A, Miles' Legion Artillery, was engaged at Pittsburg Landing, Tenn., on March 1, 1862, and was involved in the siege at Corinth, Mississippi, in May and June of that year. The battery was consolidated on June 30, 1862, with Guibor's Missouri Battery and ceased to exist as a separate unit. James Cosgrove's name does not appear on that unit's roster or the roster of any other Confederate units. Gibson's Battery was not at Murfreesboro or Gettysburg. You should look at his widow's Confederate pension application at the Louisiana State Archives to see if it contains any other information about his Confederate service.