Musk -- Twitter's new owner -- announced this week he would implement a policy charging an $8 monthly fee for users to keep their blue check badges to prove their accounts are authentic. He originally set the price at $20, but then lowered it. It's unclear when he plans to make the $8 fee official.

This didn't sit well with many critics and AOC, who sent out a flurry of Tweets Tuesday/Wednesday, giving Musk a piece of her mind.

"Lmao at a billionaire earnestly trying to sell people on the idea that 'free speech' is actually a $8/mo subscription plan," the New York congresswoman tweeted.

AOC followed up with another zinger ... "One guy's business plan for a $44 billion over-leveraged purchase is apparently to run around and individually ask people for $8. Remember that next time you question yourself or your qualifications."

She even complained that her Twitter notifications weren't working properly.

Musk then got into it with her. The Tesla/SpaceX boss tweeted a photo of an AOC sweatshirt selling on her website for $58, seemingly defending his $8 subscription fee by showing she, too, is trying to monetize her business.

But, the Democratic lawmaker wasn't having it, tweeting ... "My workers are union, make a living wage, have full healthcare, and aren’t subject to racist treatment in their workplaces. Items are made in USA."

Musk fired back ... "Your feedback is appreciated, now pay $8." AOC landed the last punch, though, declaring she had "gotten under a certain billionaire's skin" next to a laughing emoji.