I see no evidence that William M Atkinson served in the Confederate military. You should be aware that other men by this name lived in the State of Alabama in 1860. Wiliam J Atkinson who served in the 23rd Alabama Regiment lived in Pike County; William Atkinson who served in the 2nd Alabama Cavalry lived in Monroe County. If I'm not mistaken, both survived the war.

In 1913 the widow Ursula Atkinson filed an Alabama pension application for service of her husband in Co E, 15th Alabama Regiment. Her son Cornelius V Atkinson son served honorably with that command, but no one remembered his father ever joining the company, nor is there any record that he did so. The 15th Alabama Regiment belonged to the Army of Northern Virginia. After going into service the regiment never came within a hundred miles of Fort Morgan.

Also, the 1866 state census of Alabama includes information on families who lost men during the war or were crippled by wartime injuries or disease. Many of Ursula Atkinson's neighbors listed one or more family members who either died of wounds or disease during the war. She listed no one.

It would be interesting to see the pension application made by Ursula Atkinson to see what if any details of service she could offer.