A judge is expected to rule on Friday on the effort by former President Donald J. Trump and his co-defendants in the Georgia election interference case to disqualify Fani T. Willis, the prosecutor overseeing it.

The disqualification effort began more than two months ago, when a defense lawyer said in a court filing that Ms. Willis, the Fulton County district attorney, had engaged in a romantic relationship with Nathan J. Wade, the lawyer she hired to run the case.

Defense lawyers claimed that the relationship between the prosecutors presented an untenable conflict of interest, because Mr. Wade was paid more than $650,000 in public funds while he was at least partly paying for cruises and other vacations he took with Ms. Willis.

Ms. Willis acknowledged the relationship several weeks after the defense filing, and later testified that the relationship ended last summer. She and her team have sharply rebutted the idea that a conflict ever existed.

Speculation and court hearings around the relationship have since eclipsed the election case itself, which charges the former president and 14 of his allies with plotting to overturn Mr. Trump’s defeat in Georgia in the 2020 election.

The judge overseeing the case, Scott McAfee of Fulton County Superior Court, said on March 1 that he would rule on the disqualification question within two weeks.