Authority to raise a regiment of Arkansas infantry for twelve months' service was granted in November 1863 to Elisha Baxter by Maj. Gen. Frederick Steele, commanding U.S. forces in Arkansas, who shortly thereafter gave verbal permission to mount the regiment. However, Steele had exceeded his authority. The U.S. War Department had long since adopted the policy of authorizing regiments only on the basis of three years' service, and refused to accept into the service any regiment organized for a less period of time. Accordingly, the regiment was disbanded and, so far as the U.S. Government was concerned, never officially existed. None of the soldiers were ever mustered into service (at least in Baxter's regiment, though some went on to serve in other Union regiments).
The paperwork on two companies (A and B) with about 170 men was received by Steele, and subsequently found its way into the Report of the Adjutant-General of Arkansas of November 1, 1866. Annecdotal information suggests that Baxter had recruited a few more companies with about 400 men; however, the paperwork on these companies was apparently never sent forward, and those names are lost to history.
The roster published in the Adjutant-General's report lists a Pvt. John C. Merritt, Co. A, who enlisted at Batesville on January 1, 1864; but no one named Joshua C. Merritt. Given the rather slipshod history of this outfit, it is entirely possible that Joshua C. Merritt's name was erroneously recorded as John C. Merritt.
After the war there were several pension applications from men who claimed to have been in the 4th Arkansas Mounted Infantry, but whose names do not appear in the Adjutant-General's report. As far as I know, none of the applications were approved.