With less than a month to go before Robert Menendez, New Jersey’s disgraced former U.S. senatormanaloplay, is scheduled to be sentenced for corruption, his lawyers submitted an emotion-laden appeal for leniency based on what they depicted as Mr. Menendez’s hardscrabble upbringing, life of service and devotion to family.

In a legal brief filed minutes before midnight on Thursday, the lawyers, Avi Weitzman and Adam Fee, laid out Mr. Menendez’s rise to political prominence in Hudson County, N.J., and a catalog of good deeds done for constituents during three decades in Congress.

The indictment raised immediate questions about Adams’s ability to serve as mayor. He is the first mayor in modern New York City history to be charged while in office.

As they did during Mr. Menendez’s two-month bribery trial in Manhattan, Mr. Weitzman and Mr. Fee suggested that their client’s greatest failing was being led astray by a conniving wife.

Nadine Menendez, the former senator’s wife, was charged with her husband with conspiring to trade his political influence for bribes of cash, gold bars and a Mercedes-Benz convertible. Her trial is expected to start next month.

“The evidence showed that Senator Menendez was unaware of activities that Nadine was undertaking, including the receipt and sale of gold bars by Nadine, and cash she stored in her locked closet and her safe deposit box,” the lawyers wrote in their filing.

And in a letter of support also filed on Thursday, Mr. Menendez’s daughter, Alicia Menendez, a high-profile anchor on the cable news network MSNBC, hinted at the sacrifices her father continued to make for his wife, who was being treated for breast cancer.

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