A new class of New York fintech startups is going after the most basic financial product of all: the checking account. App-first challengers are courting customers with no-fee accounts, instant transfers, and budgeting tools that traditional banks have been slow to match.

The fictional startup Ledgerly, based in the Flatiron District, has signed up hundreds of thousands of users by targeting New Yorkers fed up with overdraft charges. Its founders argue the branch is a legacy cost that customers no longer want to subsidize.

Incumbent banks have responded by upgrading their own apps and cutting some fees. The competition is reshaping consumer banking in the city, even as questions linger about how the fee-slashing newcomers will ultimately make money.