The Roster of Confederate Soldiers, 1861-1865, shows:

Watkins, E.A. SC Arty. Fickling's Co.

Fickling's [or Ficklin's] Company also known as Brooks SC Arty Battery - organized in 1862 - armed with two 6-lb Smoothbores, one 12-lb Napoleon and one 12-lb Howitzer on 10/17/62 - armed with four 12-lb Howitzers 7/1-3/63 - surrendered at Appomattox Court House, VA 4/9/65
assigned Army of Northern Virginia from June 1862 to Sept 1863
Army of TN from Sept 1863 to April 1864
Army of Northern Virginia from April 1864 to April 1865
mostly with Alexander's-Huger's Battalion, Artillery

Sifakis, Compendium of the Confederate Army - South Carolina and Georgia, pages 13-14

There are three other "E. WATKINS" but all are Infantry:

Watkins, E.H. SC 22nd Inf. Co.G 1st Lt.
Watkins, Edwin SC Inf. 7th Bn. (Enfield Rifles) Co.A
Watkins, Ephraim SC Inf. Hampton Legion Co.B