Might not be either one, or neither one...

Jesse Underwood
42nd Virginia Infantry Co.B
Enlisted March 15th 1862; Floyd Co Va
Captured May 12th 1864; Battle of Spotsylvania
Held at Belle Plain, Pt Lookout, then arriving at Elmira on Aug 16th 1864
Died Jan 7th 1865 of Pneumonia
Woodlawn Grave # 1231

Jesse Underwood
60th Virginia Infantry Co.H
Enlisted July 4th 1861; Princeton, Mercer Co Va (WV)
Captured July 7th 1864 in Maryland, near Harpers Ferry
- Record notes that he vol surrendered to the 1st NY Cav near Harpers Ferry, claiming to have an Uncle residing in Columbus Ohio and stated his desire to go there.
Taken to Old Capital Prison in Washington DC, then transfered to Elmira arriving on July 25th 1864.
Died Feb 4th 1865 of Variola (Small Pox)
Woodlawn Grave #1824

There was also a James A Underwood in the same company of the 60th Va also enlisting from Princeton on the same day as this Jesse. James was Captured on Sept 19th 1864 at the Battle of 3rd Winchester. Paroled from Pt.Lookout POW camp on March 17th 1865.

Jesse Underwood
59th Virginia Infantry Co. I (2nd)
Enlisted July 15th 1861; Princeton; Mercer Co Va
Captured Feb 8th 1862 at Roanoke Island NC
Paroled Feb 21st 1862 at Elizabeth City NC
No further record in this unit
- There is an Isham and Peter Underwood also listed in the same company of the 59th Va. all from Princeton.

Its possible this "3rd" Jesse in the 59th Va "might" be the same individual as the first one above. Conscripted back into service.

1860 Census for Mercer Co Va (WV) shows two different "Jesse Underwood" both residing in Princeton area.

Jesse Underwood 28
Elija Underwood 24 (wife)
Mary Ann U. 8
Thomas J. 6
Virginia 2

Jesse Underwood 25
Martha H Underwood 25 (wife)
Lilburn 2