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.