Rich and elderly bank customers are particularly at risk, prosecutors say, when tellers and other retail-branch employees tap into accounts to wire funds without authorization, make fake debit cards to withdraw money from A.T.M.s and sell off personal information to other criminals. Accounts with high balances and those with direct deposits of government funds, like Social Security payments, are especially coveted.

“It’s a rampant problem,” said Brenda Fischer, chief of the Cybercrime and Identity Theft Bureau for the Manhattan district attorney’s office. The Manhattan prosecutor’s office estimates it brings at least one case against a teller per month.

Last year, a teller in White Plains was sentenced for her role in an identity theft ring that pilfered $850,000 from bank accounts. Wiretaps revealed that the defendants spoke in code about potential bank targets, referring to TD Bank as “touchdown” and JPMorgan Chase as “Yase.” A former teller at a Capital One branch in Maryland was sentenced in 2014 for gaining access to seven accounts and passing customer information to a co-conspirator who drew checks on the accounts.

Across the country last year, cases included a former Pennsylvania teller sentenced for withdrawing money from accounts; a former Manhattan teller sentenced for using information to receive tax refunds that he routed to himself; a former Connecticut teller who took cellphone photos of account information, and used that to cash fraudulent checks; and a former Virginia credit-union teller who took out loans from the union in customers’ names. The money she stole ultimately led to the credit union’s collapse.

Other lower-level employees who work at bank branches may have too much access to customer information, prosecutors say: In December, prosecutors in Brooklyn obtained indictments against two bankers who worked at retail locations of JPMorgan Chase in the borough, saying they withdrew roughly $400,000 from accounts through fake A.T.M. cards and in-person withdrawals.