Looks like a father/son relationship, however, I could not identify on census records

W. W. Wilkins, age 46, 3rd Lieutenant, Company L, 44th Mississippi Infantry, Capt. W. W. W. Wood's Company, Polk's Legion of Maj. Gen. L. Polk's Grand Division, Army of the Mississippi,* joined for duty and enrolled December 20, 1861 at Natchez, Miss. by Capt. Wood for the war, died at Corinth March 31, 1862

This company was assigned to Blythe's Regiment Mississippi Infantry April 16, 1862.

The 1st (Blythe's) Battalion Mississippi Infantry was mustered into service of the State of Tennessee, May 25, to July 11, 1861, and on Aug. 8, 1861, it was mustered into the Confederate States service for one year. The battalion was increased to a regiment and known as Blythe's Regiment Mississippi Infantry, this designation being changed to 44th Regiment Mississippi Infantry June 6, 1863

...........

W. W. Wilkins, age 26, 1st Lieutenant, Capt. R. T. English's Company Light Artillery, Mississippi, enlisted August 11, 1862 at Fayette, Miss. by Lieut. Lanier for 3 years, signed for a requisition for forage at Port Hudson, La. March 23, 1863, last recorded present on the March/April, 1863 muster roll at Port Hudson, signed a voucher for personal travel July 31, 1863, believe in Virginia, no further information

M269: Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Mississippi