Former New York state assemblyman Dov Hikind and Joseph Saladino, a YouTube personality running for Congress, have filed the claims.
Both cite a recent ruling against President Donald Trump, which said he was breaking the law by blocking critics on the social media platform.
The men say the law should apply to all politicians.
“Trump is not allowed to block people, will the standards apply equally?” Mr Saladino tweeted.
And a feud with House Speaker Nancy Pelosi escalated after Congress passed a border funding bill that four young Democrats opposed. Pelosi discussed the bill, and those in her party who oppose it, in an interview last weekend. She told the New York Times: “All these people have their public whatever and their Twitter world, but they didn’t have any following. They’re four people, and that’s how many votes they got.”
Ocasio-Cortez said to The Washington Post on Wednesday that the “persistent singling out” by the Speaker may be more than “outright disrespectful.”
In an earlier interview with The New Yorker Radio Hour, Ocasio-Cortez accused Congress of using women and minorities as “bargaining chips.”