Donald Trump summoned senior aides to his 26th floor office at Trump Tower around 2009 for an unpleasant task: persuade Michael Cohen—a top lawyer at his company—to resign, according to one of the aides.

Mr. Trump’s frustration had reached a breaking point, the aide said. Mr. Cohen wasn’t getting things done and Mr. Trump didn’t believe he was a good fit at the Trump Organization, even though he liked him and didn’t want to fire him. “What’s he doing here?” Mr. Trump demanded.

The message was relayed to Mr. Cohen. Visibly upset, Mr. Cohen pushed back. “I will try to prove myself,” Mr. Cohen replied, a person familiar with the matter said.

Mr. Trump eventually dropped the issue, but not before dealing another blow to Mr. Cohen by way of a big pay cut, slashing his annual income of more than $400,000 roughly in half, according to another person familiar with the matter.

The episodes, never previously reported, cast in new light the decade-long relationship between now-President Trump and Mr. Cohen. The lawyer found his niche as a fixer of some of Mr. Trump’s thornier problems, including playing the heavy with potential deal partners, and helping the real-estate developer write some of his meaner tweets.