ROME — Officials at Link Campus University, a small Rome college lined with courtyards and gravel paths, like to point out the Renaissance balcony where Pope Pius V prophesied the decisive naval victory of the Holy League over the Ottoman Empire.

They are less excited about the university’s cameo in more recent history.

In 2016, a Trump campaign aide met Joseph Mifsud, a professor at Link who is now at the heart of the Russia investigations, and he later learned from him that the Russians had Hillary Clinton’s emails.

That initial campus encounter has expanded in prominence thanks to a counterinvestigation by the Trump administration that has twice brought Attorney General William P. Barr to Rome.

Despite a lack of any evidence, President Trump has promoted, and Mr. Barr has investigated, the possibility that the professor was planted by American officials — the so-called deep state — to entrap the campaign adviser, George Papadopoulos, and prevent Mr. Trump’s election.