A deep animus had existed between the two men, prompted by a $40 million civil fraud lawsuit that Mr. Schneiderman filed against Mr. Trump’s for-profit educational venture, Trump University, in August 2013.

The filing of Mr. Gleason’s letter marked an extraordinary convergence of two of the moment’s most explosive news stories: the abrupt demise of Mr. Schneiderman, who quit his job on Monday amid allegations that he had physically assaulted four former girlfriends, and the case of Mr. Cohen, who is under investigation for potentially having broken the law by trying to suppress negative coverage of Mr. Trump in the run-up to the 2016 election.

The letter also shed new light on the simmering feud between Mr. Trump and Mr. Schneiderman, one that was inflamed anew this week as several of Mr. Trump’s supporters took to social media to revel in Mr. Schneiderman’s downfall.

As for Mr. Gleason, he is a well-known figure in New York’s legal and political circles. A former firefighter, he mounted a failed campaign for City Council in 2003 and last year briefly sought to challenge the Manhattan district attorney, Cyrus R. Vance Jr., as a write-in candidate. In his legal practice, he has shown a penchant for involving himself in salacious, tabloid-ready cases. In 2012, for instance, he represented Anna Gristina, the so-called Soccer Mom Madam, who was accused of running a brothel on Manhattan’s Upper East Side. (At a hearing in the case, Mr. Gleason offered to put up his own TriBeCa loft to help pay Ms. Gristina’s bond and told the judge that she and her family could move in with him while she awaited trial.)

In his interview on Friday, Mr. Gleason also said that he had told several elected officials of his concerns about Mr. Schneiderman’s abusive behavior nearly five years ago, but was rebuffed.