Lawyers representing former President Donald J. Trump are continuing to press their argument that the lead prosecutors in the Georgia election interference case are lying about when their romantic relationship began, surfacing phone records on Friday that they will likely use to try to undercut the prosecutors’ testimony.

In a court filing, Mr. Trump’s lawyers in Atlanta presented an affidavit describing phone records obtained through a subpoena that they said showed more than 2,000 calls between Fani T. Willis, the Fulton County district attorney, and Nathan Wade, the lawyer she hired to help oversee the case, in the first 11 months of 2021. The records also showed that the two exchanged roughly 12,000 text messages over that period.

There is no dispute that Mr. Wade and Ms. Willis were in contact in 2021. They are longtime friends, and after Ms. Willis was elected district attorney in 2020, she appointed Mr. Wade to a hiring committee to screen applicants for jobs in the district attorney’s office. She also consulted with Mr. Wade on a number of issues, including strategic questions about big cases, after taking office in January 2021.

His advisory role extended into the period covered by the cellphone data that Mr. Trump’s new motion cites, Jan. 1, 2021 to Nov. 30, 2021. At a hearing in the case last week, former Gov. Roy Barnes of Georgia, an experienced trial lawyer, recalled that Ms. Willis and a team that included Mr. Wade met with him in October 2021 and asked if he wanted to take the job that Ms. Willis eventually gave to Mr. Wade.

Ms. Willis and Mr. Wade recently acknowledged that they had been in a romantic relationship, but they said it began after she hired him to work on the Trump case

The affidavit of Charles Mittelstadt, an investigator hired by the Trump lawyers, also described cellphone location data that they said showed Mr. Wade’s phone, on at least 35 occasions, was connected “for an extended period” to a cell tower near a condominium where Ms. Willis was living.