Are there any examples where the non-believers demanding a miracle for the proof of Catholic faith and a saint succeeding in performing it? Questions: Are there any examples where the non-believers demanding a miracle for the proof of Catholic faith and a saint succeeding in performing one?

I am looking for those kinds of examples, especially if they were performed by a saint.
On more than one occasion, at Fanjeaux and Montréal, in order to resolve theological disputes between Albigensian heretics and Catholics, the Albigensians challenged St. Dominic to throw his book in the fire and they'd throw theirs in, too, and whoever's books remained unscathed would contain the truth. St. Dominic's book immediately jumped out of the fire unscathed, and the heretics' burned. St. Dominic's book is said to have defended the Immaculate Conception.
Here is how Bl. Jordan of Saxony, O.P., recounts it in his biography of St. Dominic, the Libellus:


One day a famous disputation was being held at Fanjeaux and a large number of the faithful and unbelievers had gathered. Many of the former had written their own books containing arguments and authorities in support of the faith. After these books had been inspected, the one written by Blessed Dominic was commended above the others and unanimously accepted. Accordingly, his book and that produced by the heretics were presented to three judges chosen with the assent of both sides, with the understanding that the side whose book was chosen as the more reasonable defense should be regarded as having the superior faith.

After much wrangling, the judges came to no decision. Then they decided to cast both books into a fire and, if either of them was not burned, it would be held as containing the true faith. So they built a huge fire and cast the books therein. The heretical book was immediately consumed by the fire, but the one written by the man of God, Dominic, not only escaped burning, but, in the sight of all, leaped far from the fire. For a second and a third time, it was cast into the fire, but each time it leaped back and thereby openly testified to the truth of its doctrine and the holiness of the person who had written it.



The trial by fire: the writings of the Albigenses are consumed in the flames, while St. Dominic’s book on the Flesh of Christ is miraculously borne safely away in the presence of the whole assembly. (See pages 18 and 236 [of Sr. Drane's biography of St. Dominic]). In this book St. Dominic affirmed the Immaculate Conception of the Blessed Virgin Mary.