Bankers are convicted of allowing a Putin ally to deposit millions in Swiss accounts.

GENEVA — Four bankers have been convicted of failing to conduct due diligence on Swiss accounts that were opened in the name of a musician with close ties to President Vladimir V. Putin of Russia and used to make deposits worth tens of millions of dollars.

The bankers, who led the Swiss unit of the Russian lender Gazprombank, helped to move millions of Swiss francs through two accounts opened for the musician, Sergei P. Roldugin, a concert cellist nicknamed “Putin’s wallet,” from 2014 to 2016. The bankers denied the charges.

A court in Zurich on Thursday handed the four bankers, including three Russian and one Swiss citizen, suspended seven-month jail sentences with two years’ probation. They cannot be identified for legal reasons. The judge also imposed fines amounting to 540,000 Swiss francs, about $590,000, for one of the bankers, the chief executive of Gazprombank’s Swiss subsidiary, and lesser financial penalties for his colleagues.

Mr. Roldugin is a longstanding friend of Mr. Putin and godfather to his eldest daughter. The accounts opened in his name indicated he had assets of at least $50 million and received income of over $8 million a year, the indictment said.

“The declared assets and the declared asset flows were in general in no way plausible as Roldugin’s own assets” prosecutors said in their indictment of the four bankers.

Swiss banks are required to terminate accounts when they are uncertain about the true identity of the beneficial owner. In this instance, the bankers were aware of Mr. Roldugin’s connections but conducted only the most cursory of background checks.

Gazprombank announced in October that it was pulling out of Switzerland and is in the process of closing down there. But the case has put a spotlight on the country’s role as a favorite destination for billions of dollars of deposits by Russian state and business interests at a time when the war in Ukraine is testing the limits of traditional Swiss neutrality.

The case was also seen as a test of Switzerland’s willingness to punish bankers for wrongdoing, but it has attracted criticism over what has been perceived as the leniency of the penalties imposed. Bill Browder, a British-based financier and campaigner against corruption in Russia, called the sentences “absurd” and said they were evidence that “Switzerland wants to be seen to be doing something but doesn’t want to be tough.”

Swiss prosecutors noted that Mr. Roldugin said in an interview with The New York Times in 2014 that he was not a businessman and did not have “millions.” They also observed that, officially, Mr. Putin is not wealthy “but in fact has enormous assets managed by people close to him.”