Fewer than 2% of the tens of thousands of migrants overwhelming New York City have applied for work authorizations — while no one even knows how many more are eligible to apply, The Post has learned.

Roughly about 800 adult migrants in the Big Apple have filed the proper paperwork to start earning a legal paycheck after nearly 18 months of a border crisis that left the city swamped with a wave of asylum seekers, according to data provided by City Hall.

And while the city knows there are about 40,000 adult migrants in its care, the number who are work-eligible is actually a mystery as neither the city, state or feds have properly tracked the migrants after crossing the border, the data shows.

Obtaining work authorizations for asylum seekers has been at the center of Mayor Eric Adams’s months-long push to relieve the expected $12 billion financial burden on the Big Apple, but the new snippet of data reveals how little progress has been made in getting them to work.

“That is almost like watching paint dry,” Councilman Bob Holden (D-Queens) quipped of the pace. “It’s showing that government — no matter what level, city, state and federal — isn’t cut out to handle this.”

In addition, only a quarter of the nearly 60,000 migrants currently in the city’s care have started the process to file for asylum, starting the half-year clock on making them eligible for work visas, the data shows.

The government confusion is so bad, that no city officials even know if any of the 800 migrants who applied for work visas have been granted approval, a process that the feds say can take up to two months.

The city could save up to $140 million a year for every 1,000 asylum seekers it manages to get out of the shelter city, according to estimates of migrant costs.

The city, which has been criticized by the state and feds for not gathering enough info on migrants in city care, just started last week to get details on work eligibility among the population scattered across more than 200 makeshift shelters throughout the city.

That survey, however, is expected to take weeks.

Councilwoman Diane Ayala (D-Manhattan/The Bronx), who chairs the general welfare committee, which oversees homelessness agencies, put the blame on City Hall for not doing its “homework.”

“The issue here is a lot of mismanagement, you’ve got too many hands in the pot,” Ayala said. “Everything that comes out of this administration changes from day to day.”

Adams has grown increasingly frustrated over recent weeks with the White House’s inaction and has ratcheted up his rhetoric as the Biden administration has thrown its hands up over work authorizations.

“People are critiquing how we managed the work papers, and the people who are critiquing them are seeing thousands upon thousands of people come into our country and end up in New York City?” Adams railed when asked about how the city had been tracking migrants since the start of the crisis on Thursday.

“So a crisis that is created nationally we’re looking at a local city to solve it?” he scoffed.

City Hall officials told The Post that it should be the responsibility of the federal government to track asylum seekers after they enter the country since it is an immigration issue while the city has scrambled to feed, clothe and house the thousands of migrants coming each week since spring 2022.

But after more than a year of inaction by the Biden administration, the city officials say they responded by opening its Asylum Application Help Center, which is staffed with more than 50 workers and two dozen immigration lawyers to help move along the bureaucratic process of claiming asylum and filing work authorizations.

For its part, the White House has taken no ownership of the crisis, instead taking potshots at the city and state for mishandling the mess and blaming Congress for not acting to address the broken immigration laws.

A federal assessment team that was dispatched to NYC last month slammed the city’s tracking of migrants, but City Hall has denied that criticism has anything to do with its new survey for work authorization.

The only recent bit of good news for City Hall has been the promise of 50 Department of Homeland Security staffers to help process asylum paperwork and finally, Friday, inked the deal to use Floyd Bennet Field for migrant housing.

It was unclear how many asylum seekers’ work authorizations have been filed, if any, by DHS that were not processed by the city.