The Abner Richardson in Co F 42nd VA Inf appears to be the 41 year old from Henry Co who was a Farmer and the father of Logan [P.]Richardson, age 18 in 1860, and he also was a member of Co F. This Abner Richardson married Nancy Minter, daughter of Silas Minter, Dec 19, 1838, according to the Henry County Marriage Bonds. Abner's birth was May 1819 and he died in Henry Co in 1906.

There are 11 other Richardson's in the 42nd:
Floyd, out of Henry Co who enlisted in Co F on 12 March 1862
Franklin, out of Henry Co who enlisted in Co F on 17 March 1862 and became a full musician
George, Jr who was out of Ridgeway and enlisted in Co A on 8 June 1861, promoted to 2nd Lt, resigned 6 Feb 1864
George, out of Henry Co who enlisted in Co F on 22 June 1861
Jesse, out of Ridgeway, enlisted in Co A on 8 June 1861; promoted 2nd Lt 15 June 1861; promoted Captain 21 April 1862; promoted Major 31 Dec 1863; died 5 May 1865 at Petersburg Hospital
John Sr, out of Henry Co, enlisted in Co F on 17 March 1862
John Jr, out of Henry Co, enlisted in Co F on 22 June 1861, discharged 23 September 1862
Joseph, out of Henry Co, enlisted in Co F on 17 March 1862; died 24 May 1862
Logan, out of Henry Co, son of Abner, enlisted in Co F, 13 October 1864
Peter, out of Floyd Court House, enlisted in Co B on 15 July 1862
Thomas, out of Orange Co, enlisted in Co A on 26 September 1863; promoted Full Sergeant 1 June 1864
Thomas, out of Rocky Mount, Franklin Co, enlisted in Co K on 17 June 1861; promoted 3rd Corporal 20 Sept 1862; promoted 2nd Sergeant [estimated] 1 Jan 1864; promoted 1st Sergeant 1 Mar 1864
William, out of Ridgeway, enlisted in Co A on 8 June 1861; promoted 2nd Sergeant 20 Sept 1861; reduced to ranks 5 Dec 1861

The other "Abner Richardson" I find are:

Name: Abner Richardson
RESIDENCE: Grayson County, Virginia
Enlistment Date: 7 May 1864
Enlistment Place: Dalton, Georgia
Side Served: Confederacy
State Served: Virginia
Service Record: Enlisted as a Private on 7 May 1864.
Enlisted in Company C, 63rd Infantry Regiment Virginia on 7 May 1864.

Name: Abner Richardson
Side Served: Confederacy
State Served: Virginia
Death Date: 30 May 1902
Death Place: West Point, New Kent County, Virginia
Service Record: Enlisted as a Private.
Enlisted in Company 1st, 1st Co. Howitzers Light Artillery Regiment Virginia.

Name: Abner Richardson
Side Served: Confederacy
State Served: Virginia
Service Record: Enlisted as a Sergeant.
Enlisted in Company C, 1st Reserves Infantry Regiment Virginia.

I'm not finding any "Abner Richardson" born in 1839 in Virginia but that doesn't mean there wasn't one.

There was an Anderson Richardson born in 1839 in Franklin, Virginia who married a Martha Radford in Floyd Co, Virginia on 24 April 1859 and was the son of Sampson Richardson.

JR