A three-judge panel from a federal appeals court in Manhattan heard arguments on Tuesday in a case that might sound like little more than an odd souvenir of these strange times, but that in fact raises a novel First Amendment question.

At issue is whether President Trump can block people from seeing the messages he posts on his personal Twitter account, @realDonaldTrump — something he has done a fair number of times, while also using the platform to conduct presidential business, like dismissing his secretary of state and barring transgender troops from serving in the military.

A few months into his presidency, Mr. Trump and his social media director, Dan Scavino, were sued by seven plaintiffs — all active Twitter users and ardent critics of the president — who had been blocked from seeing the president’s Twitter posts. That meant they also couldn’t reply or see other people’s responses to his tweets.

“Because of the way the president and his aides use the @realDonaldTrump Twitter account,” the plaintiffs in Knight Institute v. Trump said in their complaint, “the account is a public forum under the First Amendment.” They asked a federal judge to declare the blocking a form of “viewpoint-based exclusion” and to order that their access be restored.