The boy, who was shot in the thigh, suffered serious injuries and was taken to hospital for surgery following the shooting in Northern Avenue on Sunday afternoon.
South Yorkshire Police confirmed he was an "entirely innocent bystander".
In a statement, the boy's father said: “On Sunday afternoon my son, who is just 12 years old, was out playing with his friends, when he was shot in broad daylight. This is a shocking and horrifying thing for a parent to hear has happened to their child.
“Things are getting out of hand, people need to stop living in fear and we need to get these armed thugs off the streets. When our children are affected by violence, that is the final straw.
“I have confidence that the police are doing all they can but if you have any information that might help them please tell them, speak to them and help them with their investigation.”
Two people have since been arrested in connection with the incident.
A 25-year-old man arrested on Wednesday on suspicion of attempted murder and possession of a firearm remains in custody.
A 30-year-old man arrested on Tuesday on suspicion of attempted murder and possession of a firearm has been released on bail.
Enquiries are ongoing and anyone with information is urged to contact 101 quoting incident number 516 of 12 January 2020 or call the independent charity Crimestoppers anonymously on 0800 555111.