Richard Broughton, 37, died on Sunday after he was knocked down by a car in Elsecar at around 19:00 GMT on Friday.
The car did not stop at the scene. South Yorkshire Police has since recovered a vehicle in connection with the crash.
A 23-year-old man has been arrested on suspicion of murder, and a 35-year-old man has been held on suspicion of violent disorder.
Both men remain in custody.
Police said a disturbance was reported prior to the incident on Welland Crescent.
Officers have appealed for anyone with information to come forward.

Bakehouse Close and Riddle's Close - once home to philosopher David Hume - are among those selected for a makeover by Edinburgh World Heritage.
Fleshmarket Close, which is famously a setting for an Inspector Rebus novel, has also made the final list.
Lighting and artwork will be installed in the little-used closes.
The people behind the project hope the improvements will encourage more people to use the historic network of narrow streets.
Adam Wilkinson, the director of Edinburgh World Heritage, said: "Our aim is for this project to re-connect the people of Edinburgh with the closes of the Old Town.
"The intricate network of closes and courtyards that bind the Old Town together gives it a unique identity, is underused but has the opportunity to be revitalised, used and celebrated by all."
The closes date back to the medieval origins of the city.
Originally, individual plots of land were set up lining the main street, with paths to gain access to the land behind.
As each plot became built up over time, so they developed into narrow lanes connecting courtyards and streets behind the Royal Mile.
The Twelve Closes project was welcomed by city leaders, including John Thompson, of the Old Town community council.
He said: "This is a project to be welcomed, changing dilapidated and neglected closes into useful routes linking different parts of the Old Town.
"The closes were once busy thoroughfares, buzzing with all the life of the city, and it would be wonderful to see some of that atmosphere return."

Republicans ambushed a mini-bus carrying the men at Kingsmill in County Armagh in 1976 and murdered them after checking what religion they were.
Senior coroner John Leckey is retiring this year and told a preliminary hearing of the inquest in Belfast that no replacement has been appointed.
His retirement could leave only one coroner in Northern Ireland.
Kingsmill is among dozens of inquests dating from the early days of the Troubles that face delay because not enough money is available to investigate or there is nobody to oversee fresh hearings.
Mr Leckey said: "I feel for the bereaved families, not exclusively Kingsmill but for other inquests I am involved in.
"It is a disappointment that is widespread."
A lawyer for some of the Kingsmill victims' families said they would be pressing Stormont's justice department for more resources to allow an inquest to go ahead.
Karen Armstrong, a sister of one of the murdered men, said the lack of resources was "a political problem".
"We are not going to lie down and accept it," she said.
"We will fight until we get another date and they have to make sure there are enough coroners in Northern Ireland to deal with our and many other cases."
Ulster Unionist MLA Danny Kennedy said he would be asking Justice Minister David Ford to ensure the matter was referred to the relevant authorities so that "action can be taken as soon as possible".
"Justice has been denied for almost 40 years and it is totally unacceptable that this inquest should be delayed further due to the unavailability of a coroner," he said.
"This was one of the most shocking and cruel events of the Troubles and the inquest must be treated with the seriousness this crime merits."
A Department of Justice spokesman said: "Officials are actively working to ensure that all necessary resources are provided for the conduct of inquests in Northern Ireland.
"There are currently three full-time coroners in Northern Ireland. In addition, one High Court judge and one County Court judge have also been appointed as coroners."
Two men have been arrested following an alleged hit-and-run in Barnsley.
[NEXT_CONCEPT]
Twelve of Edinburgh's "dilapidated and neglected" closes are to be transformed as part of a major project to improve the Old Town.
[NEXT_CONCEPT]
An inquest into an IRA massacre of 10 Protestant workers has been delayed because there is no coroner to hear it.