hortly after he became attorney general last year, William P. Barr set out to challenge a signature criminal case that touched President Trump’s inner circle directly, and even the president’s own actions: the prosecution of Michael D. Cohen, Mr. Trump’s longtime fixer.

The debate between Mr. Barr and the federal prosecutors who brought the case against Mr. Cohen was one of the first signs of a tense relationship that culminated last weekend in the abrupt ouster of Geoffrey S. Berman, the United States attorney in Manhattan. It also foreshadowed Mr. Barr’s intervention in the prosecutions of other associates of Mr. Trump…

Mr. Barr spent weeks in the spring of 2019 questioning the prosecutors over their decision to charge Mr. Cohen with violating campaign finance laws, according to people briefed on the matter.

At one point during the discussions, Mr. Barr instructed Justice Department officials in Washington to draft a memo outlining legal arguments that could have raised questions about Mr. Cohen’s conviction and undercut similar prosecutions in the future, according to the people briefed on the matter.