In the listing of soldiers buried in the Cedar Hill, Vicksburg City Cemetery, is this listing:

Jones, Jacob, Co. C, 1st Arkansas Battery*, died 21 Jun 1863
(Most likely 1st Arkansas Cavalry Battalion as there was no 1st Arkansas Battery at Vicksburg, Carried in the UDC Record as Janes, Jacob)

* It would appear that someone down the line mistook the
abbreviation, Battn [Battalion] as Batt [Battery]

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Jacob Jones

Residence was not listed;
Enlisted as a Private
"C" Co. AR 1st Battn Cavalry

Sources used by Historical Data Systems, Inc.:
- Index to Compiled Confederate Military Service Records

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1st Battalion, Arkansas Cavalry (Stirman's)

1st (Stirman's) Battalion Sharpshooters, formerly Brooks' 1st Arkansas Cavalry Battalion, was organized during the summer of 1862. The unit was attached to General M.E. Bgrann's comman, Department of Mississippi and East Louisiana, and fought at Port Gibson and Vicksburg where it was captured on July 4, 1863. After being exchanged, it returned to Arkansas and became Stirman's Arkansas Cavalry Battalion. The unit was commanded by Lieutenant Colonel Henry W. Bridges and Ras. Stirman, and Major Lafayette Boone.

Predecessor unit:

1st (Brooks') Cavalry Battalion was organized during the late fall of 1861. In January, 1862, it totalled 300 officers and men and was assigned to L. Hebert's Brigade in the western part of Arkansas. After fighting at Elkhorn Tavern, the unit was ordered east of the Mississippi River and dismounted. It now became known as Stirman's 1st Arkansas Battalion Sharpshooters. Major William H. Brooks was in command.
NPS Soldiers and Sailors System, http://www.civilwar.nps.gov/cwss/regiments.cfm

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Jacob Jones, Company C, 1st Battalion Arkansas Cavalry (Stirman's), enlisted March 11, 1862 in Crawford County by Capt. M. O. Davidson, recorded present on the Jan. & Feb., 1863 muster roll,* last paid December 31, 1862, no other records

* This is the only and only muster roll surviving for Company C which was stationed at the time at Camp Donalson, Miss. None of the other companies of the battalion have subsequent records either.

M317: Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Arkansas

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At the time of his death, his Battalion was attached to Bowen's Division, Green's Brigade, assigned to Green's Redan, anchoring the right flank of the Stockade Redan Complex on the siege line.

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Information on the Vicksburg campaign is best found in Edwin Cole Bearss' 3 Volume work, The Campaign for Vicksburg, Morningside Books, 1986

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See also:

http://www.couchgenweb.com/civilwar/stirmdx.htm
http://civilwarroster.com/cw/rosters/stirmans.html
http://www.google.com/search?client=safari&rls=en&q=1st+Battalion+(Stirman's)+Arkansas+Cavalry&ie=UTF-8&oe=UTF-8