I know that Graves' Btty. is listed in some references on Chickamauga, but I'm not sure why. The battery was formed as the Mississippi "Issaquena" Artillery, but while at Bowling Green in the fall of 1861 it was assigned to the Kentucky Orphan Brigade, and became known as Graves' Ky. Btty.
The battery went to Fort Donelson and was captured there, and when the men came back out of prison, the battery was not reconstituted as it had been. Or at any rate, it was not re-armed, and most of the men went into Cobb's Ky. Btty. before Murfreesboro. I have not seen any official records that list this battery after Nov. 1862. Perhaps another battery was raised under Selden Spencer, who had commanded the Mississippians in Graves' Btty., but I don't have any info on this.