Kath is going to face the reds’ wrath.

Mayor Mamdani’s socialist cronies vowed to target Gov. Kathy Hochul to push her on their “tax the rich” crusade — as the comrades boasted they “control” the Big Apple.

Democratic Socialists of America leader Gustavo Gordillo warned Hohcul that the emboldened far-left group will target her next after their candidates upset establishment Democrats in several key races in Tuesday’s party primaries.

“She knows we’re coming for her,” Gordillo told the New York Times.

The warning came after Mamdani-endorsed DSA congressional candidates Darializa Avila Chevalier and Claire Valdez, along with avowed progressive Brad Lander, swept their Democratic primary races Tuesday.

The red sweep across those three diverse Big Apple congressional districts covering parts of Manhattan, Brooklyn and the Bronx prompted a jubilant Osman Chaudhary, co-chair of the New York City DSA Electoral Working Group, to claim a socialist mandate.

Chaudhary rattled off a lengthy list of Big Apple neighborhoods, including the “People’s Republic of Ridgewood” and the “People’s Republic of Astoria” — both located along the city’s so-called “Commie Corridor” — under the DSA’s sway.

“We have a democratic socialist mandate in New York City,” he said on a DSA call Wednesday night.

“Don’t even try it. We control these areas, we won by massive margins,” he also told those considering challenging the DSA politicians, according to a clip shared on social media by Stu Smith, an investigative analyst at the conservative Manhattan Institute think tank.

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The wins also signaled both Mamdani’s power as a political kingmaker and the growing influence of the far-left faction within the Democratic Party.

Hochul, a moderate, last year endorsed Mamdani in hopes of harnessing the far-left fervor that swept him to victory in New York City’s mayoral race. She quickly moved to placate the socialist phenom by supporting his push for universal childcare and doling out billions of dollars to help close a yawning city budget shortfall.

But she held firm against Mamdani’s — and the DSA’s — demand that she support raising taxes on the wealthy during this year’s state budget process. Still, critics have wondered if she’d fold to the pressure after she faces voters in the November elections and begins a new budget process.

The governor’s opposition to the hike and continued embrace of Mamdani has led to several awkward moments in which crowds of fired-up DSA diehards have tauntingly chanted “tax the rich” at her.

“Taxing the rich is a top priority of our slate and one of the key policies they ran and won on,” a DSA rep told The Post on Sunday.

Gordillo, who co-chairs the DSA’s Big Apple chapter, told the Times that if Hochul wins re-election this year that she should expect a renewed push — and added pressure from the faction’s adherents in Washington, DC.

“I think we have to show New York what it means to have three democratic socialists in the congressional delegation,” Gordillo said, according to the Times.

All but two of Hochul’s own endorsements in the primary ended up falling to DSA-backed candidates – a sign her stature as the state’s Democratic Party leader didn’t hold a candle to Mamdani’s own growing influence.

“Everyone is furious,” one Democratic insider said about establishment party members. 

“She created part of this problem, and it’s going to bite her in the ass.”

Mamdani’s endorsements targeting establishment Dems stoked fears before the primary that he was fueling an intraparty civil war between far-left DSA acolytes and moderates such as Hochul. After the primary, insiders said the whole state Democratic Party could be facing a leftist takeover.

“The lesson tonight is that it’s Zohran Mamdani’s party and we are just voting in it,” said Evan Roth Smith, a campaign consultant, Tuesday evening.

“We should not just expect more congressional challenges, but more assembly and senate and council challenges. We should expect the DSA to remake the Democratic Party in New York. The old system of clubs and country parties, to what the DSA has built and Mamdanii has at his disposal, he remade New York City politics.”

Beyond pressing Hochul on taxing the rich, many lefty Dems also set their sights on toppling House Minority Leader Hakeem Jeffries – a moderate who frequently frustrates radicals with his play-it-safe political style.

“Jeffries is not invincible. He has a target on his back in 2028,” said Corbin Trent, a former staffer for firebrand Rep. Alexandria Ocasio-Cortez who worked on her campaign that toppled establishment Dem fixture Rep. Joe Crowley in 2018.

City Councilman Chi Ossé geared up to challenge Jeffries during the primary, but dropped his bid after pushback from Mamdani and narrowly lost a bid to gain the DSA’s backing.

But after Tuesday’s primaries, DSA true believers appeared to have second thoughts on not challenging Jeffries.

“Chi would have won,” Gordillo posted on X as results streamed in Tuesday night.

State Republicans blasted the Democrats’ seeming socialist takeover, casting it in apocalyptic terms. 

“The DSA isn’t just a faction within the Democratic Party anymore — it is the Democratic Party in New York, and Kathy Hochul, Chuck Schumer, and Hakeem Jeffries are too weak to stop them and too afraid to condemn them,” said state Republican Party Chairman Ed Cox.

“This is a group that has hosted rallies for Hamas, wants boys competing in girls’ sports and views the free market and nuclear family as things to be dismantled.”

Mamdani, when asked Wednesday about taxing the rich, said his priorities haven’t changed. He did, however, offer praise for Hochul’s past help.

“I’ve also been honest with New Yorkers about what I believe is necessary to deliver on that affordability, and I’m proud to be standing here speaking about 2-K (childcare), which is only possible because of the partnership we have with Gov. Hochul,” he said.

Hochul’s re-election campaign officials declined to comment on DSA leaders warning they’re coming for her. They instead referred The Post to a statement from state Democratic Committee Chair Jay Jacobs.

“New York Democrats are united and ready to win this November with a slate of proven leaders who are fighting to lower costs, protect healthcare, make our communities safer, and stand up to Donald Trump’s attacks on New York,” Jacobs said.

Hochul and Mamdani appeared at several events in the city Thursday but left without taking questions from reporters.

– Additional reporting by Matthew Fischetti, Vaughn Golden and Patrick Reilly