He may served with the 8th. Confederate Cavalry.
CWS&SS lists a Private J.L. Mathews in Company A, 4th. Battalion Mississippi Cavalry which became a part of the 8th. Conf. Cavalry in 1862.

Excerpt from the history of the 4th. Battalion @
http://www.mississippiscv.org/MS_Units/4th_Bn_MS_CAV.htm

The battalions of Baskerville, Brewer and Bell, six Alabama and four Mississippi companies, were merged as the Eighth Confederate Cavalry, William B. Wade Colonel, Jefferson Falkner Lieutenant-Colonel, John T. Wright Major, succeeded by John S. Prather. Part of Chalmers' Cavalry force which attacked Sheridan's Cavalry at Booneville, July 1, 1862, and won a victory with considerable loss.

With the beat system within a county, how do you go about finding what geographical area a beat covers?

You might try this message board and also ask for a cemetery lookup in case he was brought home to be buried.
http://boards.ancestry.com/mbexec?htx=board&r=rw&p=localities.northam.usa.states.mississippi.counties.pontotoc