Your William Braden did serve in the 3rd Battalion Mississippi Infantry. You will also find him originally (I believe) in the 27th Alabama Infantry. The 3rd Miss. Battalion was later called the 45th Mississippi and Company I made up of Capt. Wright’s Company of the 27th AL Infantry. I am going to list some of the info from his service records and his info from the Alabama Civil War Soldiers Database. I suggest you take this info to Alan Pitts who can be contacted from one of his post here on this forum. He's the man for Alabama soldiers. Meanwhile I can tell you your man was sick it seems the whole time he is serving. He was captured May 7, 1863 at Raymond, Mississippi. He is listed among those captured in the Vicksburg campaign and is shown being paroled from Fort Delaware yet his service record up through DEC 1863 shows him as "sick in Vicksburg". That would mean he was P.O.W. there. Yet according to his alabama info he was paroled in 1865 so he evidently has more records somewhere. I'll keep looking

If the final notes down at the bottom are correct it seems he survived the war and was alive at least until the 1907-1908 census. It's a confusing search for me but I bet Alan can sort it out. Meanwhile here are my notes. Hope this helps.

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3rd Battalion Mississippi Infantry
(Note: Company I of this battalion was from Alabama)

Roll APR 16 to JUN 30, 1862
Enlisted DEC 27, 186? at Florence, Alabama
Absent: Sick at General Hopsital

Roll dated JUL & AUG 1862
Absent: sick

Name appears on a roll of prisoners of war paroled at Fort Delaware JUL 3, 1863
(Roll not dated)
Captured near Raymond May 7, 1863

27th Alabama Infantry
Muster Roll dated NOV & DEC 1863
Enlisted DEC 16, 1861
Remarks: Sent to Vicksburg sick

Muster Roll dated SEPT & OCT 1863
Sent to Vicksburg sick

Roll dated JUL & AUG 1863
sent to vicksburg sick

Roll Undated
Captured July 4, 1863 Vicksburg
Paroled: Not dated
________________________________________

Last Name: Braden
First Name: William MI:
Date of Birth: 1840/12/03
Birth Information: USA, Alabama, Spring Valley
Date of Death:
Death Information:
Marital Status:
Occupation:
Enlistment Date: 1862/04/00
Enlistment Information: Tennessee, Fort Henry, Private
Engagements:
Engage. con't:
Remarks: Discharged June 1863. Reenlisted (June) in Company G 33rd Mississippi Regiment at Tupelo, Mississippi. Consolidated with the 49th Regiment and was with them until close of the war. Paroled May 1865. Address 1907-8: Spring Valley, Alabama
Remarks con't:
Other Info:
Discharge Date: 1863/06/00
Discharge Information:
Branch: Infantry
Regimental Unit: 27th Alabama Regiment
Company Unit: B
Co. Unit Name:
Pension Rec:
Authority: Census, Tax Collector, Colbert County, Alabama 1907-8