The incidents took place in the 1990s, but they did not come to light until last year.
Blame was directed at two former employees. One is dead and the other left the service in 1994.
Two of the allegations were investigated by the gardaí and referred to the Director of Public Prosecutions.
In the third case, the Brothers of Charity Service South East said the gardaí could not fully investigate it as the person involved opted not to make a statement.
“It is our understanding that the Garda investigation arising from allegations made by two of the complainants resulted in the submission of a report to the Director of Public Prosecutions. The DPP decided not to proceed with a prosecution,” it said.
The details of the cases emerged in documents released under the Freedom of Information Act. These showed the board of Brothers of Charity Service South East was briefed in April last year about the emergence ofa number of allegations dating back to the 1980s and the 1990s.
The board was told that protocols had been followed in the handling of the cases.
“The complaints that the chief executive advised the board by way of information related to historical allegations of sexual and physical abuse of three adults by two former employees of the Brothers of Charity Services,” the service said in a follow-up statement.
“In line with standard protocols, we promptly notified the Health Service Executive and An Garda Síochána of these allegations.”
Until now, allegations of sexual abuse by adults in the care of the service had not been known.
The incidents of child sexual abuse, detailed in the Ryan Report, were largely from the period before 1990.
In 1999, Brother Denis Quirke pleaded guilty to two counts of indecency and assault of a boy between 1985 and 1987. This related to abuse that occurred in the south east.
However, he had been under effective house arrest since those allegations first surfaced in 1990.
Other child abuse reports regarding services run by the order have emerged since the publication of the Ryan Report. However, it was believed these related to periods in the 1970s and 1980s.
In 2011, fresh allegations surfaced about the neighbouring Brothers of Charity service in Cork.
The Commission to Inquire into Child Abuse said the order’s handling of abuse allegations at Lota, Cork and its protection of an abuser was a serious indictment on the order.
“The Congregation kept records about sexual abuse allegations concerning lay people, and routinely involved the gardaí,” said the commission. “The situation was different for Brothers. The allegations were dealt with internally, and no records were kept, or else were kept in codified language.
“For this reason, factual information about the true extent of sexual abuse did not exist, and abusers were left free to abuse again.”