Cohen has a verified account on Twitter — that's when you have a following and they confirm you are who you say you are. That means his tweets got to the top of the president's feed. Cohen set up an alert so that he could know when Trump tweeted.
"If I replied right away, I could get lucky and have a lot of people read my tweets," he says.
But then, one day the president blocked him. Cohen was surprised. He says he wasn't trolling the president.
"I was basically civil," he says. "I didn't use a lot of profanity. I didn't harass people individually. I mostly made graphical memes with slogans on them like 'corrupt,' 'incompetent,' and 'authoritarian.' "
Cohen says that once he was blocked, his tweets about the president reached fewer people. So he believes the blocking is censoring his ability to criticize the government.
Cohen is now one of the plaintiffs in a groundbreaking lawsuit brought by the Knight First Amendment Institute at Columbia University.
Katie Fallow, a senior attorney at the institute, says the suit is based on long-standing First Amendment principles, "where if the government opens up a space or hosts a kind of public forum where they allow the public to speak, they can't exclude someone from that forum based on their views."
The Twitter account @realDonaldTrump is the president's personal account. It was created before he became president. But Fallow says the president has used it to make official announcements.
"Like the replacement for the FBI director after he fired James Comey, and the transgender ban," as well as a lot of other policy announcements, says Fallow.
But it isn't just that Trump uses the account to make official announcements. He also uses it to interact with the public.
Josh Geltzer, the founding executive director of the Institute for Constitutional Advocacy and Protection at Georgetown University Law Center, says it's like a virtual town hall.
The institute filed a brief in support of the blocked Twitter users. He says you can exclude people from a town hall for lack of space, but not for their opinions. He points to a recent case in Virginia where a federal court found the country could not block an individual from an official county Facebook page.
Geltzer says the case was similar to this one. He says the county was trying to "shut out voices that weren't obscene or bullying, but voices that simply expressed criticism or unwanted viewpoints."
No one from the Justice Department was available in time to speak to NPR. However, in its brief, the government argues that this is the president's private Twitter account. He's using it just like everyone else. Twitter is a private platform with its own rules. The president has a right to block people.