South Yorkshire Police said officers were alerted to disorder in Doncaster Road, Conisbrough, at 5.40pm on Saturday and found that violence had flared between students from different schools.
Some of those involved were carrying weapons at the time, with the aunt of one of the victims claiming he was stabbed.
Inspector Dan McKnight, of South Yorkshire Police, said: "From our initial enquiries, we understand this to be a pre-arranged incident between groups of youths from separate schools.
"Their behaviour on Saturday evening was unacceptable, putting both theirs and the wider community’s safety at risk, so we are working closely with the schools concerned to identify those involved.
"We believe that some of those individuals involved in Saturday night’s disorder may also have been carrying weapons, which is simply unacceptable.
"Someone could have been gravely injured as a result of the actions of this group, which is important for those youths involved to remember.
"The consequences to being involved in such violence can be severe, and we want to reassure the community that we’re taking this matter very seriously indeed.
"We are currently following up a number of lines of enquiry and I’d urge anyone with information to come forward and talk to police. If you were involved on Saturday evening, or know who was involved, please make yourselves known to either staff at your school, your family or to officers so we can arrange to come and talk with you."
Five arrests were made.
Anyone with information should call South Yorkshire Police on 101 quoting incident number 844 of January 20.
Crimestoppers can also be contacted on 0800 555 111.