Michael D. Cohen, President Trump’s former lawyer and fixer, told Congress on Wednesday that Mr. Trump had instructed him to send threatening letters to his alma maters, warning of jail time for anyone who released his transcripts.

“I’m talking about a man who declares himself brilliant but directed me to threaten his high school, his colleges and the College Board to never release his grades or SAT scores,” Mr. Cohen said, part of broad testimony he gave before the House Oversight Committee.

One of those letters was sent to Fordham University in May 2015, a month before Mr. Trump declared that he was running for president. Mr. Trump attended the university for two years before transferring to the University of Pennsylvania.