When officers arrived on the 700 block of State Street, they found two men had been stabbed and a third man had other injuries.
Elijah Sommerville, 33, of Stone Mountain, Ga., was treated for injuries he received during the altercation.
The other men, Anthony Brummitt and Chris Robinette, both of Bristol, Tenn., were treated at Bristol Regional Medical Center for apparent knife wounds, Price said.
Investigators have a warrant for Sommerville’s arrest on two counts of malicious wounding.
Police did not say what the men were fighting about, but the investigation is continuing and there could be more charges.