The schools are among the most recognizable Catholic institutions in New York, with reputations extending far beyond the church’s followers and the city’s borders: Xavier, Regis, Brooklyn Prep, Fordham Prep. They educated many in the city’s Catholic elite, producing politicians, authors, academics and at least one Supreme Court justice. They regularly appear on lists of New York’s best Catholic schools.

But on Tuesday, the schools’ names popped up again and again on a different kind of list: One naming Jesuit priests who were identified by the Society of Jesus as having a history of sexual abuse found to be “more likely true than not after investigation.”

In some cases, the priests passed through the schools in careers that spanned as many as 30 years.

The lists of accused priests were published by the Jesuit order one after the other in recent weeks, creating rosters of several hundred names. The Society of Jesus, as the Jesuit order is known, is an influential force in the global church; it has more than 16,000 members, including Pope Francis.

The latest list names priests who served in the order’s province covering the Northeastern United States, most of whom served in Jesuit schools.

The Jesuits have contributed to a flood of names that have surfaced in recent weeks as dioceses and religious orders across the country have sought to move toward transparency. The disclosures come as the Catholic Church confronts a wave of investigations by law enforcement officials on the federal and state levels, as well as a crisis of confidence among followers shaken by the church’s handling of sex abuse.

Advocates said victims racked with shame and anguish have received long-awaited affirmation as the church shines a glimmer of light on cases that have been shrouded in darkness and denial.

“This new transparency by the church is a good thing for victims, naming priests who are predators,” said Mary McKenna, a leader of the New York City chapter of Snap, or Survivors Network of those Abused by Priests. “It validates the victims and helps them heal.”

The Jesuit order is known for its emphasis on education, and it has long operated schools, including some of the most respected colleges and universities affiliated with the Catholic Church.

Last year, the Society of Jesus said it would release the names of all of its clergy across the United States who were the subject of credible abuse claims. Since December, several hundred Jesuits have been identified in abuse allegations dating as far back as the 1950s.

The Northeast province, the last to make its disclosure, named 50 men who have faced at least one allegation the order considers credible. Most of the accusations involved Jesuits working in schools or serving in parishes.

At least nine of them were assigned to Boston College High School around the time of the suspected abuse. Many of the others passed through Canisius High School in Buffalo and McQuaid Jesuit in Rochester during their careers.

One of the longest-serving priests on the list, Cornelius Carr, served in at least seven schools from 1945 to 1993, and worked in parishes until 2005, when he was accused of abuse that took place about 15 years before. He died in 2013.

Outside of the Jesuit disclosures, at least 35 Catholic dioceses in the United States have published accused priests’ names. The pace accelerated substantially after the explosive grand jury report released in August by the Pennsylvania attorney general’s office that detailed the abuse of more than 1,000 people by hundreds of priests.

Critics have raised doubts over how complete the lists are, as the dioceses and orders were making the disclosures at their own discretion. In some instances, victims have pointed out names they believed were absent.

“One thing missing from this list is what the immediate response by Jesuit officials was to the allegations,” Zach Hiner, the executive director of Snap, said in a statement. “Were the complaints investigated? Were they reported to police? Were priests immediately removed in response? The answers to these questions will be critical to fully understanding not only the scope of the crisis, but what changes must be made in order to prevent future cover-ups and put the safety of children front and center.”

Jesuit officials said the allegations largely came to their attention decades after the abuse, as many victims came forward after 2002, when the church’s handling of sex abuse in the United States first swelled into a crisis.

Ms. McKenna said the church’s actions, like denying abuse and transferring priests, “make the victims suffer more and re-victimize them.” She added that many victims had been threatened and traumatized. “It takes years for them to come forward.”

In the latest disclosure, the most recent claim of abuse was made in 1996. In his letter, Father Cecero, of the Northeastern province, said the order has adopted more stringent practices to prevent abuse.

Father Cecero said credibly accused Jesuits have been removed from ministry. Those who remain in the order serve in roles that involve no interaction with children, he said, and live under a “closely monitored safety plan.”

“Changed practices do not erase past history,” he said, adding, “Any case of abuse is shocking and a profound failure. Jesuits who have offended can no longer offend. Safeguards put in place since 2002 help create safe environments for everyone.”

At least 35 priests on the list have died, and others have been defrocked, permanently removed from ministry or restricted from serving in public roles.

Some names on the list, like Eugene O’Brien’s, were previously known. Mr. O’Brien was accused of molestation while he was principal and president of Fordham Prep in the 1970s, according to advocacy groups and legal records.

In 1997, the order and the Archdiocese of New York settled a lawsuit brought by the accuser for $25,000. Mr. O’Brien, who was removed from ministry in 2002, admitted to abuse that started in the 1960s, according to the order’s disclosure.

But advocacy groups assailed officials at Fordham Prep in 2008 for allowing Mr. O’Brien and Roy Drake, a priest who is now deceased but also on the list, to live on campus.

Other names on the Northeast’s list were not public until now, or their mentions were limited to discussions on victims’ online message boards.

John L. Farrand, a priest who admitted to abuse in 1961, worked at Brooklyn Prep until 1972 and served in schools until 1997. He died in 2003.

Thomas Denny, a priest accused of abuse that occurred in the 1960s and 1970s, served in three high schools in New York City, as well as schools in Rochester, Puerto Rico, Jersey City and Buffalo. His final posting was at a parish in Lagos, Nigeria.

Another priest, John T. Ryan, had worked as an editor and writer for America Magazine, the Jesuits’ weekly publication.

Mr. Ryan, who left the order, was accused of abuse that took place in the 1980s and 1990s, when he worked for the Jesuit Seminary & Mission Bureau in New York and the magazine.

Mr. Denny, Mr. Ryan and Mr. O’Brien were not reported on the list as deceased.

In a letter published Tuesday, the Rev. Matthew F. Malone, the magazine’s president and editor in chief, said he learned of the allegations last week.

“The public disclosure of this information,” he wrote, “is a necessary step toward justice and reconciliation for the victims and survivors of sexual abuse at the hands of clergy.”