An inmate was killed Friday at Hays State Prison, the third in a month's time.
But Georgia Department of Corrections officials are mum on whether any of the deaths are related.
The inmate -- who hasn't been identified -- was killed Friday afternoon. Authorities said the incident prompted them to lock down the maximum-security prison in Trion, Ga.
The Georgia Bureau of Investigation has been called to investigate the apparent homicide, GBI spokesman John Bankhead said.
Some family members of inmates said Friday they are frightened by the rash of killings and want to have their relatives transferred from the prison.
"I've got a loved one there," said Renee Sission, whose nephew is in Hays. "I'm really concerned. I don't know what to do."
The week of Christmas, Derrick Stubbs, a 25-year-old armed robber, was beaten so severely he died from his injuries a few days later. Damion MacClain, a 27-year-old armed robber, was strangled in his bed late at night after the doors should have been locked.
Families of both men told the Chattanooga Times Free Press that they had received threatening phone calls from inmates asking for money before their loved ones were killed.
State corrections officials have said the extortion claims are under investigation, but they wouldn't talk about them.
One person has been arrested in connection with MacClain's death. Daniel Ferguson, a convicted murderer already serving a life sentence, was charged with murder.
The GBI hasn't revealed any details about Stubbs, who was in protective custody when he was found dead.