I found the following:

Booth (pp 1110-1111) – Records of Louisiana Soldiers - 1920

Williams, W. B. (also on Rolls as Williams, William), Pvt. Sergt. Co. A, 6th La. Inf. En. Camp Moore, May 28, 1861, or June 4, 1861. Present on Rolls to Oct., 1861. On List dated Camp Carondelet, Va., Hdqrs. 8th Brig. A. P., March 4, 1862, Remustered for the War, February 7, 1862. Rolls from May, 1862, to August, 1862, Present or absent not stated. Rolls from September, 1862, to February, 1863, Present. Roll March and April, 1863. Absent, missing since April 29, _. Roll May and June, 1863, Absent, wounded, and absent in Gen. Hospl. Roll July and Aug., 1863, Absent, wounded at Winchester and now in Fairview Hospl., Lexington, Va. Roll Sept. and Oct., 1863, Absent on furlough. Roll Nov. and Dec., 1863, Present. Roll Jan. and Feb., 1864, Absent on furlough. Rolls from March, 1864, to Oct., 1864, Absent on detailed duty at Lynchburg, Va., by order Gen. Lee, Order No. 107. Roll of Prisoners of War, C. S. A., Paroled Lynchburg, Va., April 13, 1865.

Williams, William, Musician Co. H, 6th La. Inf. Record copied from Memorial Hall, New Orleans, La., by the War Dept., Washington, D. C., June, 1903, En. Camp Moore, La., June 4, 1861, born New York, occupation seaman, Res. New Orleans, La. Remarks: Deserted Feb. _, 1862.

NPS-CWSS – www.itd.nps.gov/cwss/soldiers.cfm

1. William B. Williams – Pvt/Sgt Co. A - 6th Louisiana Infantry – M378-Roll 31
2. William Williams – Pvt Co. H - 6th Louisiana Infantry – Musician – M378-Roll 31

NARA-CSR M320 – www.footnote.com

William B. Williams – Pvt/Sgt - Co. A – 6th Louisiana Infantry – 40 Cards in file

Capt. Arthur McArthur, Jr.’s Co. – Union and Sabine Parish Rifles

Enlisted at Camp Moore May 28 or June 4, 1861

Re-mustered for war – Feb 7, 1862

Mar-Apr 1863 - Exchanged prisoner

Absent, missing since April 29, 1863

Paroled prisoner of Army of Portomac – Aril 29, 1863 – Captured near Fredricksburg

Moved from Old Capitol Prison to Fort Delaware for exchange

Wounded and Captured June 13-14, 1863 – Winchester, VA

Wounded and absent in General Hospital

Jul-Aug, 1863 – Wounded at Winchester, VA and at Fairview Hosp, Lexington

Sep-Oct 1863 – Absent on furlough

Jan[Feb 1864 – Absent on furlough

April 18, 1864 – Detailed by order Genl Lee Special Order 107 in Lynchburg

Sep-Oct 1864 – Detailed as Provost Guard in Lynchburg (Hosp Guard)

Nov-Dec1864 – Detailed as Provost Guard in Lynchburg (Hosp Guard)

Surrendered at Lynchburg, VA by Genl Lee, April 13, 1865

William Williams – Pvt/Musician – Co. H – 6th Louisiana Infantry – 2 Cards in file

Enlisted June 4, 1861 – Camp Moore

Deserted Feb 4, 1862

Hope this helps

Don Parker