The New Jersey secretary of state has scheduled a hearing Monday to make Sen. Ted Cruz prove he is eligible to run for president under the Constitution, after a Washington-area law professor filed a challenge arguing his Canadian birth makes him ineligible.

Victor Williams, the man challenging Mr. Cruz, is also running as a write-in candidate for the Republican nomination in New Jersey, which he hopes gives him an extra boost as he tried to convince the state both that he has standing to challenge, and that Mr. Cruz should be disqualified.

Mr. Williams‘ argument is that Mr. Cruz filed a false certificate of eligibility along with the signatures he filed to get on the ballot in New Jersey.

“The certificate is false and the signatures were collected by fraudulently representing Mr. Cruz eligible,” said Mr. Williams, who founded DisruptiveJustice.org and is also a clinical assistant law professor at Catholic University.

Mr. Cruz’s Cuban father and American mother were living in Canada at the time of his birth, making him a dual-citizen and feeding into questions about whether he qualifies as “natural born” under the Constitution’s requirement for president.

“Ted Cruz’s Canadian birth certificate on public record incontrovertibly proves, that he was, and is, a natural-born Canadian. it is simply a physical impossibility for him to be both a natural-born Canadian and a natural-born American,” Mr. Williams says in his challenge.

Mr. Cruz’s campaign didn’t respond to an email seeking comment, but he has repeatedly dismissed any legal danger from his birth. He renounced his Canadian citizenship ahead of his presidential run.

Most legal scholars say Mr. Cruz is on safe ground, but several high-profile scholars say it’s not a slam dunk.

So far, no courts have ruled against Mr. Cruz. Several have dismissed challenges on technical grounds, while Pennsylvania courts ruled affirmatively in his favor, saying that being a citizen from birth meets the Constitution’s strictures.

“It is inconceivable that the Framers intended to exclude a U.S. citizen at birth from holding the office of president, simply because of where he or she happened to be born. After all, that individual is not a ‘foreigner’ — but rather, a U.S. citizen from birth,” Mr. Cruz’s lawyers said in briefs filed in one of the federal cases.

Donald Trump, Mr. Cruz’s chief competitor for the GOP presidential nomination, has raised the matter of Mr. Cruz’s birth — just as he challenged President Obama’s eligibility based on long-discredited questions about the president’s birth certificate.

That makes Mr. Williams‘ challenge all the more interesting, as even though he’s planning a write-in campaign in New Jersey, he’s a supporter of Mr. Trump’s bid.

Complicating matters is the state of affairs in New Jersey, where the election division falls under Secretary of State Kim Guadagno. She is also the lieutenant governor — sharing the ticket with Gov. Chris Christie, a former presidential candidate himself. Mr. Christie has now endorsed Donald Trump, who is Mr. Cruz’s chief rival for the GOP nomination.

Ms. Guadagno’s office didn’t respond to a request for comment Friday, though her office has accepted Mr. Cruz’s petition to run in the June 7 primary.

Mr. Williams, who has filed as a write-in candidate in several states including New Jersey, said it was striking that none of Mr. Cruz’s other competitors for the GOP nomination, even Mr. Trump, chose to challenge his birth legally.

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