You might double check the 1860 census.
George Martin
A. B. Short, age 49, enlisted as a Private in Company B, Lay's Regiment of Cavalry April 18, 1864 at Union Church, his companies muster roll dated July 2, 1864 does not record if he was present, under Remarks it notes "Recruited in the enemys lines Jefferson County Miss." no further records
Note: Union Church is in Jefferson County
A. B. Short, Private, Company D, 3rd Battalion Mississippi Cavalry Reserves, resident of Jefferson County, Mississippi was paroled at Columbus, Mississippi May 16, 1865
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A. B. Short, Private, Company F, 27th Mississippi Infantry, enlisted May 6, 1861 in Wiliiamsburg/August 26, 1861 at Brookhaven, Mississippi, discharged December 13, 1861
Williamsburg is in Covington County in which the 46th Mississippi was raised
A. [Archy] B. Short, Private, Company B, 46th Mississippi Infantry, enlisted February 22, 1862 at Williamsburg, Mississippi, captured at Vicksburg July 4, 1863, recorded as absent without leave from August 23, 1863
See: http://members.tripod.com/smsghs/Projects/project1.htm
http://www.gwest.org/46thmsin.htm