South Yorkshire Police said the Parson Cross neighbourhood policing team has been dealing with an increased number of anti-social behaviour reports around the Asda, Farmfoods and Learning Zone part of the estate.
The force said groups of youths congregating in the area and who are involved with nuisance or anti-social behaviour “will not be tolerated”.
“All of those who are identified will be dealt with robustly; banning orders will be issued, behaviour contracts enforced, and where crimes have been identified the offenders will be prosecuted,” the force added.
“We have a long-term plan progressing to address some of the issues we face in this area and hopefully we will be in position to share this with you soon.
“As a team, we take incidents of this nature extremely seriously and recognise the damage it can cause to the confidence of our community as well as the long-term consequences for the youths themselves.
“In recent weeks we have seen a further incident of youth-related anti-social behaviour in this particular area and unfortunately this has escalated to criminal damage and public order related offences.
“Our officers have stepped up patrols in this area and we have worked extensively with partner agencies to identify those involved.”
PC Alice Boucher added: “We have already dealt with a significant number of these young offenders and will continue to deal robustly with anyone found to be involved with anti-social behaviour or more serious offences in this area.
“Many local addresses have been visited, parents spoken to and 10 youths will be interviewed at the station and processed this week.
“My message to parents within our community is to please consider where your sons and daughters are, who they are spending time with, and what they are doing when they are out of the home – it came as a shock to some of those we visited this week who now face a trip to the station with their children.
“Our enquiries into a number of other reports remain ongoing and officers are compiling evidence to identify and deal with those involved.”