Lynn, I don't know of any battalion history of the 4th Arkansas Battalion, but since they operated almost continually with the 4th Arkansas Regiment after Shiloh (indeed were eventually consolidated with the regiment), any references you find to the 4th Arkansas Regiment and McNair's Arkansas Brigade (Army of Tennessee) can be assumed to apply also to the 4th Arkansas Battalion.

I have a few items related to the 4th Arkansas Battalion, which I'll post when I dig them out. I have a list of the battalion's movements and stations from the Spring of 1862 to the Winter of 1863, a couple of casualty lists, and a few other things.

As a matter of interest, the 4th Arkansas Battalion was organized with five companies, but Capt. Frederick William Hoadley's Co. D, from Pulaski County, was detached early on and served as a heavy artillery battery in the 1st Tennessee Heavy Artillery Regiment. Captain Hoadley was promoted to major in the regiment and was killed in action at Vicksburg.