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 that Ms. Willis’s office challenged later in the day, Mr. Trump’s lawyers in Atlanta presented an affidavit describing phone records obtained through a subpoena that they said showed “just under 12,000” calls and text messages 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 affidavit from Charles Mittelstadt, an investigator hired by Mr. Trump’s lawyers, also described cellphone location data that the lawyers said showed Mr. Wade’s phone, on at least 35 occasions, being connected “for an extended period” to a cell tower near a condominium where Ms. Willis was living.

The investigator said the data suggested that on two occasions, Mr. Wade was in the vicinity of Ms. Willis’s residence from late at night until dawn. One of those occasions was on the night of Sept. 11, 2021.

Ms. Willis’s office responded with its own filing on Friday night, saying that the records “do not prove that Special Prosecutor Wade was ever at any particular location or address.” The response also said that the phone records showed only that Mr. Wade “was located somewhere within a densely populated, multiple-mile radius where various residences, restaurants, bars, nightclubs and other businesses are located.”

The district attorney’s office included copies of some of Ms. Willis’s emails and calendars that it said refuted specific claims made by Mr. Trump’s legal team about her whereabouts.

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

Mr. Trump’s lawyers did not release the data used by their investigator, so it was not possible to immediately verify their claims amid their shifting accounts of what the data revealed.

The original affidavit claimed that the two exchanged roughly 2,000 calls and 12,000 text messages over those 11 months in 2021. But later on Friday, Mr. Trump’s lawyers released a corrected affidavit that removed the reference to the 12,000 total text messages, and instead claimed that “just under 12,000 interactions” occurred between the two lawyers. The updated affidavit defined “interactions” as including voice calls and text messages.

It was also not clear on Friday what effect Mr. Trump’s filing might have on the defense’s ongoing effort to disqualify Mr. Wade, Ms. Willis and her entire office based on allegations that the romantic relationship led to a conflict of interest.

But the records will almost certainly be used by defense lawyers to argue that the two prosecutors began their romantic relationship before Ms. Willis hired Mr. Wade on Nov. 1, 2021 — and not in 2022, as the two prosecutors have insisted.

The reliability of such cellphone tracking technology has come under fire before, including when it was deployed by allies of Mr. Trump to help advance false claims about widespread ballot stuffing during the 2020 election. Such technology can be limited in how precisely it can pinpoint someone’s location.

The relationship first came to light in a filing last month by Michael Roman, one of 15 co-defendants in the election interference case and a former Trump campaign official. Mr. Roman contends that the two prosecutors engaged in “self-dealing” behavior that amounted to a conflict of interest, because Mr. Wade used money he was paid by the district attorney’s office to fund trips that he and Ms. Willis took together.

Ms. Willis and Mr. Wade have denied any improper financial benefits, and have testified that they roughly split the costs of their vacations.

But the question of exactly when the relationship started has also become a matter of contention, with Mr. Roman’s lawyer claiming that it started before November 2021 — which would mean, in essence, that Ms. Willis hired a boyfriend for the lucrative and high-profile job of managing the Trump case.

The lawyers are scheduled to continue arguing over the disqualification question in a hearing set for next Friday.

Anthony Michael Kreis, a law professor at Georgia State University who has followed the Trump case in Georgia closely, said he doubted that the cellphone data would factor heavily into the judge’s ruling on disqualification. Because Ms. Willis has acknowledged that Mr. Wade was a mentor and close adviser, Professor Kreis said, “it’s not contradictory for them to spend time together and exchange text messages, especially in the run-up to the investigation of Donald Trump.”

Still, Mr. Kreis said the data “could be problematic” if the judge believes that it damages Mr. Wade’s and Ms. Willis’s credibility.