Albany’s new pay rules come with a string attached: legislators will only get their fat annual raises in 2020 and 2021 if they pass Gov. Andrew Cuomo’s budget proposals for those years on time.

“Essentially the governor is saying, ‘If you vote for this I will personally give you $10,000,’” Assemblyman Michael DenDekker (D-Queens) told The Post. “And isn’t it funny that this is falling in the two years when he could be running for president?”

“This requirement is incredibly detrimental to the legislature as a coequal branch of government,” said Jadan Horyn of Reclaim New York, a good-government group. “It’s both a stick and a carrot that does not belong in the governor’ hand.”

DenDekker told colleagues he’ll abstain from the budget vote in protest, he said.

“But I told them, ‘I hope you all vote for it so I can get my $20,000.’”