But for the challengers, running — even with a near-guarantee of defeat — has few downsides. They can raise thousands off Ms. Ocasio-Cortez’s name alone; earn exposure for future campaigns; and bask in the attention, even if only for a short time.

For her part, Ms. Ocasio-Cortez has used the swell of challengers as fund-raising fodder.

In an email to supporters soon after the Republican candidates’ contribution numbers were reported, Ms. Ocasio-Cortez’s campaign announced an “emergency goal” of nearly $850,000 — the sum of the Republicans’ hauls — for October. If met, Ms. Ocasio-Cortez would be on track to raise more than $2.5 million in the next quarter.

By contrast, in New York’s 15th Congressional District, which borders Ms. Ocasio-Cortez’s, only one candidate has raised more than $400,000 in a quarter, even though the race is considered competitive: The incumbent, Representative José Serrano, has announced his retirement.

It is unclear how much support the challengers to Ms. Ocasio-Cortez will receive from their party establishments. Traditionally, state and local parties back incumbents, but Ms. Ocasio-Cortez has rankled fellow Democrats with her and her supporters’ unabashed willingness to back primary challenges against longtime officeholders.

In a recent fund-raising email, Ms. Ocasio-Cortez’s team wrote that ever since her victory, “corporate Democrats have been waiting for their chance to strike back.”

The Queens County Democratic Party — the longtime power base of former Representative Joseph Crowley, whom Ms. Ocasio-Cortez defeated — did not return a request for comment on Ms. Ocasio-Cortez’s primary challengers.

One of the Democratic challengers, Fernando Cabrera, a New York City councilman, said he consulted the Bronx County Democratic Party’s chairman, Assemblyman Marcos Crespo, before announcing his campaign.