For what it's worth - skimming through the Roster of Confederate Soldiers using 3rd VA Lt Arty indicates a "Local Defense" unit.

Sifakis, Compendium of the Confederate Armies - Virginia, page 4

3rd VA Artillery Regiment, Local Defense Troops - aka 2nd Arty Reg, Local Defense Troops - organized 3/5/1862 - disbanded May 1862 - many members enlisted in 28th VA Inf Bn
First Commander: John C. Porter, Col
Field Officers: James B. Dorman, Maj
John C. Shields, Lt Col
Assigned: Field's Brigade, Aquia District, Department of Northern Virginia - April-May 1862