Same name, but different man. This William Jeffreys was a Columbia County man who was an original member of Co. E, 11th Arkansas Regiment; was sent back to Arkansas on sick furlough; and was detained in the Trans-Mississippi by order of Hindman and assigned to Co. G, 33rd Arkansas Regiment. He died of disease in hospital at Monroe, Louisiana, on July 25, 1863.

I can't find any further record of Allen's William Jeffreys in any Arkansas regiment.