As President Trump was leaning toward appointing Amy Coney Barrett to the Supreme Court five years ago, some advisers shared doubts about whether she was conservative enough. But he waved them away, according to someone familiar with the discussions. He wanted a nominee religious conservatives would applaud, and with an election approaching, he was up against the clock.

Soon after Justice Barrett arrived at the court she began surprising her colleagues. Chief Justice John G. Roberts Jr. assigned her to write a majority opinion — among her first — allowing the seizure of state property in a pipeline case, according to several people aware of the process. But she then changed her mind and took the opposite stance, a bold move that risked irritating the chief justice.

In another early case, as Justice Samuel A. Alito Jr. tried to further his decades-long quest to expand the role of religion in public life, she preferred a more restrained route, setting off a clash in their approaches that continues. And in a key internal vote, she opposed even taking up the case that overturned Roe v. Wade and the federal right to abortion, though she ultimately joined the ruling.

Now Mr. Trump is attacking the judiciary and testing the Constitution, and Justice Barrett, appointed to clinch a 50-year conservative legal revolution, is showing signs of leftward drift.

She has become the Republican-appointed justice most likely to be in the majority in decisions that reach a liberal outcome, according to a new analysis of her record prepared for The New York Times. Her influence — measured by how often she is on the winning side — is rising. Along with the chief justice, a frequent voting partner, Justice Barrett could be one of the few people in the country to check the actions of the president.