A lawyer for one of the defendants charged along with former President Donald J. Trump in the Georgia election interference case said in a court filing on Monday that the district attorney overseeing the case, Fani T. Willis, had engaged in a “clandestine” relationship with the special prosecutor she hired to help handle it.

The filing, from a lawyer representing Michael A. Roman, a former Trump campaign official, provided no proof of the relationship or other claims it contained. It argued that the relationship should disqualify Ms. Willis, her office and the special prosecutor, Nathan Wade, from prosecuting the case.

The defense lawyer, Ashleigh B. Merchant, also wrote that Ms. Willis, the district attorney in Fulton County, Ga., was “profiting significantly from this prosecution at the expense of the taxpayers,” charging that Ms. Willis and Mr. Wade had taken vacations together with money he made working for her office.

Citing “information obtained outside of court filings,” Ms. Merchant wrote that Ms. Willis and Mr. Wade “have traveled personally together to such places as Napa Valley, Florida and the Caribbean” and that Mr. Wade had bought cruise ship tickets for them.

Ms. Merchant also argued in the filing that Ms. Willis had not obtained the proper approval to appoint Mr. Wade and that the case should be dismissed as a result. Mr. Wade is one of several outside lawyers whom Ms. Willis’s office is paying to help with the Trump case, a complex racketeering indictment against 15 people.

It is unclear how the claims will affect the Georgia prosecution, one of several criminal cases against Mr. Trump. The former president filed a flurry of motions in the case on Monday, including one in which his lawyers argued that he is immune from prosecution in the case.

Clark D. Cunningham, a law and ethics professor at Georgia State University, reviewed Mr. Roman’s filing and questioned why it did not contain any proof of a relationship between the two prosecutors.

“If Roman’s lawyer has actual evidence of an improper relationship between Willis and Wade, it was incumbent on her to make that part of her motion, such as by attaching sworn affidavits from witnesses with personal knowledge or authenticated documents,” he said in an email.

Ms. Merchant, in a phone interview, said that she had reviewed documents showing that Mr. Wade and Ms. Willis had traveled together to vacation destinations and that Mr. Wade had paid for some of the tickets. She said she believed the records were included in Mr. Wade’s sealed divorce filings. She asked in a separate court filing this week that those records be unsealed.

The claims by Ms. Merchant were reported earlier by The Atlanta-Journal Constitution. They appeared in a 39-page motion filed in Fulton County Superior Court on Monday on behalf of Mr. Roman, who as a Trump campaign official in 2020 took part in a plan to organize pro-Trump electors in Georgia despite Mr. Trump’s defeat there.

Mr. Roman has been charged with seven counts, including conspiracy to commit forgery and violation of Georgia’s racketeering law.

Jeff DiSantis, a spokesman for Ms. Willis’s office, said only that the office would “respond appropriately in court.”

Ms. Merchant, in the motion, wrote that it had not been “filed lightly.”

“Nor is it being filed without considerable forethought, research or investigation,” she added.

According to her filing, “sources close” to Ms. Willis and Mr. Wade confirmed to Ms. Merchant that the two had an “ongoing, personal relationship” that began before Ms. Willis hired Mr. Wade to oversee the Trump case.

The filing states that Mr. Wade, who has his own private practice, has earned more than $650,000 for his work with the prosecutor’s office.