But prosecutors allege 66-year-old Jones may be responsible for killing up to 60 children, the New York Times reports.
The former nurse has been indicted on murder charges for the death of 2-year-old Rosemary Vega in September 1981.
Last month, Jones was also indicted on a separate murder charge for the death of 11-month-old Joshua Sawyer in 1981, by injecting him with a “toxic level” of an anti-seizure drug. The nurse was working in pediatric intensive care at the time.
Bexar County District Attorney Nico LaHood told The New York Times they will be looking into previous child deaths in Texas, where there is no statute of limitations for murder.
“It was unconscionable that she was suspected of up to 60 murders, and everyone felt they could not do anything,” he said.
“Our intention is to hold her accountable for as many deaths as the evidence will support.
“But we have to have the evidence. So we will continue to work within the confines of the law to do that. We are going to take one at a time. I am fairly confident we are not going to get 60 indictments on her, but we will get as many as the evidence supports.”
USA Today reports Jones has been dubbed the "killer nurse”.
In 1985, she was sentenced to 99 years in prison for the death of 15-month-old Chelsea McClellan. She was also convicted for the attempted homicide of a boy, just four weeks old.
Jones has always maintained her innocence.