Ryan Durkin, aged 15, was struck by a stolen silver BMW on Brinsworth Lane, Brinsworth, at around 11pm on Friday, April 19.
A black Seat Ibiza also travelling along Brinsworth Lane then collided with Ryan as he lay in the road.
The driver of the BMW failed to stop at the scene.
A GoFundMe page set up to help support his family has already raised more than £5,600 since it was set up.
A message on the page said: “After the devastating tragedy that occurred in the late hours of Friday, April 19, we are hoping that our community are able to raise funds to help support the family of Ryan throughout this difficult time.
“We would be highly appreciative if donations could be made, however small they may be. All proceeds will go directly to Ryan’s mother. Let’s come together as a community and unite.”
Sheffield United fan Ryan was taken to Sheffield Children’s Hospital with life threatening injuries but he died one week later, on Saturday, April 27.
A sea of floral tributes, balloons and Sheffield United merchandise adorn railings on Brinsworth near to where he was killed.
Andy Richie, chief executive officer of the LEAP Multi Academy Trust, which runs Brinsworth Academy, which Ryan attended, said: “We are all deeply shocked and saddened by the tragic death of Ryan.
“News of this tragedy has been felt across the academy and the whole Brinsworth community. The loss will be felt for a considerable time.”
He added: “Ryan was a quiet, popular student with a fun sense of humour.
Floral tributes on Brinsworth Lane in Rotherham to Ryan Durkin who was killed by a hit-and-run driver in a stolen car. Picture: Scott Merrylees
“He had great potential and a bright future ahead of him, particularly in sport, where he was a crucial member of the school football team.
“He will be remembered by staff as a polite, well-mannered student with a wonderful smile.
“Ryan was part of a very close knit group of loyal friends, who always look out for each other. We will continue to provide support to those needing it, in the coming weeks, as they deal with the loss of their friend.
“Our thoughts and condolences go out to Ryan's family and friends at this time.”
Mitchell Hughes, 24, of no fixed abode, has been charged with causing a serious injury through dangerous driving and failing to stop after a road traffic collision.
He has also been charged with aggravated burglary, possession of an offensive weapon and wounding, relating to an incident on Friday, April 12, when the vehicle involved in the Brinsworth collision was stolen.
Anyone with information should call South Yorkshire Police on 101 and quote incident number 1099 of April 19.
For more information or to donate to support Ryan’s family visit https://uk.gofundme.com/ryan-durkin