This should get you started. The NPS Soldiers and Sailors System cited below does contain a list of men in the unit, rather limited data. If you seek
additional information on anyone soldier, I have a subscription database which can provide a little more information. From there, you would need to obtain their service record files.

A Goggle search "3rd Battalion Georgia Sharpshooters" will yield some additional information.

George Martin

CONFEDERATE GEORGIA TROOPS

3rd Battalion, Georgia Sharpshooters

3rd Battalion Sharpshooters was organized during the spring of 1863 with men who transferred from other Georgia units and those recruited in Richmond and Gwineet counties. It contained five companies and was soon ordered to Virginia. Assigned to General Wofford's Brigade, it moved with Longstreet but was not engaged at Chickamauga. After serving in East Tennessee the battalion returned to Virginia, fought in the battles of The Wilderness, Spotsylvania, and Cold Harbor, then was part of Early's operations in the Shenandoah Valley. Placed under the command of General DuBose, it later was active in the Appomattox Campaign. The unit had many captured at Sayler's Creek and surrendered with only 1 officer and 22 men. Its commanders were Lieutenant Colonel Nathan L. Hutchins, Jr., and Majors Philip E. Davant, William E. Simmons, and H.H. Smith.
[http://www.itd.nps.gov/cwss/regiments.cfm]

See also: http://www.colquitt.k12.ga.us/gspurloc/Cobbslegion/gasca/units/3rd_bttn_sharpshooters.htm