Some New York City public school parents are out of free childcare this September after being turned down for 3K seats — and even offered spots that don’t exist, The Post has learned.

Availability has not kept up with demand throughout the city, with 500-student waitlists in some neighborhoods — and 3K offers being given for Department of Education schools that no longer have the program.

Children born in 2020 are eligible but only some districts have enough seats for all of them.

This year, more than 40,000 applications citywide poured in for the toddler program, which has room for roughly 55,000 citywide — but seats in areas in ritzier parts of the Big Apple fill up much more quickly than those that are not.

Taiba Hosseini learned this week her 3-year-old son wouldn’t have somewhere to go in the fall — even though she was initially told he was accepted at a school in Whitestone, Queens.

“They were like, ‘No, we never had an agreement with the DOE. I don’t know why they’re giving you guys this option,’” Hosseini said.

After dozens of calls to her district’s Welcome Center, which handles admissions, she was told 3K is not mandated and she is not guaranteed a seat — despite getting the offer letter online.

“There is nothing welcoming about these Welcoming Centers … they washed their hands of it,” Hosseini said.

Hosseini was referred to nearby options in people’s homes, not the established institutions she had researched.

Now, she’s hoping for one of the nearby seats she is on a waitlist for, but might not find out until October. “I would’ve paid for a spot in a school had I known, but now I’m in a position where they’re filled.”

Mayor Adams and Schools Chancellor David Banks have emphasized quality over quantity in the program, which was estimated to cost taxpayers around $470 million for 2022-2023.

“Families are choosing between, ‘Do I send them to a school that’s not safe, warm and nurturing because I need child care or go to private school?’” said one Upper West Side mom whose 3-year-old daughter wasn’t offered any seat in her district.

“I don’t know what we’re going to do, I keep thinking it’s not real,” said the mom, who said tots born at the height of the pandemic need the in-person interaction the programs provide.

“My daughter’s speech was so delayed, she didn’t start talking until after she was two, just because she hadn’t been around that sort of interaction,” she said.