Cooper, whose name surfaced soon after the 1 p.m. shooting in a campus building, had been booked at 10:41 p.m. on charges of aggravated assault and possession of a firearm on school grounds.
The jail did not provide his Augusta address.
He is accused in the shooting of JaJuan Lawayne Baker, 21, of Wilmington, N.C., on the third floor of Haygood-Holsey Hall, a building housing classrooms and Paine’s administrative offices.
Baker, who suffered a gunshot wound to the left side of his head, above the ear, was taken to Georgia Regents Medical Center, police said.
At a Monday news conference, authorities said Baker's wound was serious and he was in critical condition. Early police statements had indicated his wound was not life-threatening.
Paine has announced a noon candlelight vigil today at the Gilbert-Lambuth Memorial Chapel.