This is the correct one in Booth's "Records" on Page 1100:
"Williams, Jesse M., Capt. Col. Co. D, Field and Staff, 2nd La. Inf. En. May 11, 1861, New Orleans, La. Present on all Rolls to April, 1862. On Hospl. Register, Admitted Oct.12, 1862, to No. 5 U. S. A. Gen. Hospl., Frederick, Md. Sent to Gen. Hospl., Oct 13, 1862. Roll to Oct., 1862, Absent, wounded at Sharpsburg, Md., Sept. 17, 1862. Left prisoner in hands of the enemy. Roll Nov. and Dec., 1862. Absent on furlough in Louisiana, wounded in Sharpsburgh. Roll Jan. and Feb., 1863. Absent, wounded, on leave. Roll March and April, 1863, Present. Roll May and June, 1863. Absent, Comdg. Brigade. Rolls July, 1863, to Oct. 1863, Present. Roll Nov. and Dec., 1863, Absent, sick. Roll Jan. and Feb., 1864, Present. Roll to August 31, 1864, Killed in action May 12, 1864, Spottysylvania C. H." Then in the Confederate Veteran, Octobert 1924, issue, page 393, article, "A Slave's Devotion," states that at death of Dr. Hogan (sic., should be Private William R. K. Hogan, died May 3, 1863), his servant, Levy Carnine,remained as the servant of Capt. Jesse Williams. However General(sic) Williams was killed on the field of battle, and Levy again buried a master in a soldier's grave and returned to the regiment...." So Capt. Jesse Williams was likely buried near place of death, unless at a later date he was reinterred elsewhere.