This is the only William Webb I find in the 35th Mississippi:

William M. Webb, Private, Company A, 35th Mississippi Infantry, enlisted February 26, 1862, captured at Vicksburg, Mississippi July 4, 1864, paroled July 8, captured at Allatonna, Georgia, October 5, 1864, received at Camp Chase, Ohio prison camp October 24, 1864, subscribed to the Oath of Allegiance to the U. S., and released, June 11, 1865 at Camp Chase, description, resident of Kemper County, Mississippi, dark complexion, dark hair, grey eyes, 5' 7-1/2", age 26

M366: Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Mississippi

See also: http://www.mississippiscv.org/MS_Units/35th_MS_Inf.htm