Stephen Heeley, 26, of Leicester Road, Dinnington, and Michael Hall, 44, of Worksop Road, Rotherham, were both charged with violent disorder and possessing a blade/sharply pointed article in a public place.
Liam Hancock, 33, of Caperns Road, Rotherham, was charged with violent disorder and attempting to cause grievous bodily harm.
All four men have been remanded in custody and will appear at Sheffield Crown Court on 8 October.
Two people, a 30-year-old woman and a 54-year-old man, who were arrested on suspicion of assisting offenders have been bailed pending further inquiries, police said.