Hard-hit New York is getting the shaft in the federal government’s first round of coronavirus relief funds for doctors and hospitals, a new study found — just as local lawmakers feared.

Payments to medical facilities in the state that has borne the brunt of the COVID-19 pandemic will amount to less than $12,000 per patient as the first tranche of $30 billion in aid is distributed, a Kaiser Health News analysis revealed Friday.

But states where the illness remains rare will be getting much more: over $300,000 per reported COVID-19 case in Montana, Minnesota, and Nebraska, and a whopping $470,563 per patient in West Virginia.

“New York’s hospitals are getting hit harder by the coronavirus than anywhere in the country and should get priority,” Rep. Tom Suozzi (D-Nassau) told The Post this week. “We’re the epicenter of the pandemic.”

New Jersey providers will get just over $18,000 for each of its coronavirus cases, while Connecticut’s share will be close to $39,000.

The cash is flowing from the $150 billion in emergency grants set aside by Congress in its $2.2 trillion coronavirus stimulus package to help medical providers buy protective gear like masks and gowns.

But the federal Health and Human Services Department is using a one-size-fits-all formula to hand out the program’s first $30 billion, giving money based on providers’ 2018 payments from Medicare — not on their coronavirus caseloads.

The funding formula “allowed us to make initial payments to providers as quickly as possible,” an HHS spokesman said.

The next batch of payments “will focus on providers in areas particularly impacted by the COVID-19 outbreak,” the agency promised.