House GOP lawmakers are demanding New York Supreme Court Justice Juan Merchan’s daughter turn over documents to the House Judiciary Committee as they probe allegations of a conflict of interest in his Manhattan trial.

In a letter Thursday to Loren Merchan, House Judiciary Committee Chairman Rep. Jim Jordan, Ohio Republican, said she must turn over communications her progressive consulting firm, Authentic Campaigns, had relating to the prosecution of former President Donald Trump.

Mr. Jordan asked for any correspondence or communication between her firm and the Democratic National Committee or President Biden’s reelection campaign.

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Her deadline is Aug. 8.

Mr. Jordan noted two of Ms. Merchan’s clients, California Democrat Rep. Adam B. Schiff and Senate Majority PAC, profited $93 million from fundraising off Mr. Trump’s prosecution.

“At a minimum, there is a perception that you and Authentic Campaigns could profit considerably from President Trump’s prosecution in a forum overseen by your father,” the letter read.

Judge Merchan declined to recuse himself from overseeing the New York trial against Mr. Trump.

Allies of the former president have argued Judge Merchan should have recused because his daughter works for a marketing firm that was profiting from the prosecution and that he himself had donated to Mr. Biden, who was the presumed Democratic nominee and thus Mr. Trump’s November opponent during the trial.

A New York law requires that a judge must recuse if someone within the sixth degree of relation has an interest in the proceeding.

But Judge Merchan stayed on the case and issued a gag order against Mr. Trump preventing him from commenting about the court, its family members, prosecutors and witnesses during the trial.

Mr. Trump is still unable to comment about the court, the prosecutors or their families even after his conviction. His sentencing is scheduled for Sept. 18.

Mr. Jordan said his committee needs the documents as it explores legislation that would allow presidents to remove local prosecutions to a more neutral federal venue to avoid political bias.

The trial overseen by Judge Merchan in May resulted in the historic conviction of Mr. Trump — the first time a former president has faced criminal charges that have gone to trial. He was found guilty of all 34 counts.

Prosecutors led by Manhattan District Attorney Alvin Bragg said Mr. Trump used personal attorney Michael Cohen to pay $130,000 to adult film actress Stormy Daniels before the 2016 presidential election because she was shopping a story about an alleged sexual encounter with Mr. Trump in Lake Tahoe in 2006.

They argued it ran afoul of a New York law concerning falsifying business records with the intent to conceal a crime.