Just before midnight on Saturday, officers were called to a report of a firearm discharge on Washington Road.
A man is believed to have entered a property and shot a man in his 20s - he received minor injuries as a result.
The gun was located and seized at the scene by officers.
A number of warrants have been executed at addresses in Thurnscoe and Bolton-upon-Dearne as a result.
On Wednesday night, a 30-year-old man was arrested and he remains in custody as part of ongoing enquiries.
Detective Inspector Mark Cockayne said: “I know this incident will have no doubt caused some concern in the community but I want to reassure those residents that we’ve been working to find who was responsible.
“A team of detectives have been out gathering information and evidence all this week to get to the bottom of what may have happened.
“Anyone with information is asked to report it online or by using our live chat on our website, or call 101 quoting incident number 1025 of March 11.
“Alternatively, contact Crimestoppers anonymously on 0800 555 111.”