Up to 250 homes on the Fitzwilliam Estate have seen the tariff rise from 7.61p to 8.72p per kwh after the new meter was put in place two years ago.
A petition has started in a bid to force the authority to cut the charges.
The council said it would "assess a full year of costs" and "provide a pro-rata refund for any surplus generated".
The average tariff by the big six major energy companies is between three and five pence per kilowatt an hour.
Natasha Howe, 23, a working mother of two who lives in a three-bed detached bungalow on the estate, started the campaign because residents were "struggling with paying the bills and have been forced into fuel poverty".
"I want the tariff to be lowered," she said.
"Since the new system was put in place there's been a massive difference.
"It's costing about £150 a month to run your heating for four hours a day.
"People could run their house at 30 degrees paying £15-£20 a week running it 24/7 and now they can't run that for four hours a day. I've got people in wheelchairs suffering, in pain because they can't afford to [pay for] it.
"I'm now having to find £150 to £200 a month to pay for my heating. My last month's bill for heating alone was £156 and I've woke up this morning and found it's not even working.
"We're in 2017, we shouldn't be choosing food over heating."
Rotherham Council said: "We are aware of the concerns regarding heating bills on the Fitzwilliam Estate and appreciate that some bills appear to be unusually high.
"We are therefore exploring possible reasons for this with tenants and have already been in contact with anyone who has raised issues with us."
People living in a part of Rotherham have said they are being "forced into fuel poverty" since a new prepaid meter system was installed by the council.