The Independent Democratic Conference has maintained such payments are allowed by a clause that allows payment for service in any “special capacity therein or directly connected therewith,” though the law lays out exact dollar amounts payable to leaders in other positions.

In at least three cases — in 2015, 2016 and March of this year — Senate payroll officials have sent certified lists identifying the three senators as leaders of their respective committees. In 2015 and 2016, two documents identified Mr. Valesky as chairman of the Health Committee, requesting two payments totaling $7,500. He received the stipends, though he was and remains the committee’s vice chairman.

Earlier this year, Ms. Savino was made vice chairwoman of the Codes Committee by the independent Democrats’ leader, Senator Jeffrey D. Klein, who represents parts of the Bronx and Westchester County. Mr. Peralta, who defected to the conference from the minority Democrats in January, was made vice chairman of the Energy and Telecommunications Committee on March 7.

Two weeks after that, a member of the Senate payroll staff sent an email to the comptroller’s office with a “Senate certification” of members’ owed stipends, and a request that checks be sent out in early April. A list that was attached identified Mr. Peralta as the chairman of the energy committee, and Ms. Savino as the Codes Committee chairwoman, asking for payments of $9,375 to Mr. Peralta and $13,500 to Ms. Savino.

Both amounts were paid in early April, as were smaller stipends in March. In total, Mr. Savino and Ms. Peralta received $30,500 this year, before taxes, for positions they did not hold. The same holds true for Mr. Valesky, who received $30,000 in gross pay for the stipends in 2015 and 2016.