This is hardly the first time the two men have clashed.

Mr. Schneiderman was elected attorney general in 2010, succeeding Mr. Cuomo, who was elected governor. But Mr. Cuomo did not support Mr. Schneiderman’s bid in the primary for attorney general.

And while Mr. Schneiderman is said to want Mr. Cuomo’s job someday, Mr. Cuomo has at times seemed to want to hold onto part of Mr. Schneiderman’s.

Not long after they both took office, the governor set up a new agency, the Department of Financial Services, that conspicuously overlaps the duties of the attorney general in its pursuit of financial wrongdoing, and installing a loyal and aggressive Cuomo lieutenant to lead it.

Mr. Schneiderman has found ways to make a name for himself. In his three years as the state’s top law enforcement officer, he has won major victories in health care and succeeded in closing a loophole that allowed firearms to be sold at gun shows without background checks. In 2012 alone, he announced more than $335 million in Medicaid fraud recoveries.

On Wall Street, he was a central player in concluding the JPMorgan litigation, recently brought a high-profile case against the asset manager BlackRock, and has been forceful in challenging financial data providers that release potentially market-moving information to favored subscribers ahead of others.

“In just three years in office, Attorney General Schneiderman has revitalized virtually every aspect of his office, making it a more effective champion for fairness and equality for all New Yorkers,” his spokesman, Damien LaVera, said. “We’ll stack Attorney General Schneiderman’s track record against any of his predecessors any day.”

Still, Mr. Schneiderman has not earned the kind of hard-charging “sheriff of Wall Street” image that Mr. Cuomo and, before him, Eliot Spitzer, gained in the job.