According to the Dictionary of Apparitions of the Virgin Mary, throughout history only 6 popes have witinessed apparitions of the Virgin Mary. The weakness and insufficiency of the sources do not permit appropriate discernment. Here is the chronological list:
• Pope Liberius (356)
• John I (Saint, †526)
• Honorius III (1227)
• Honorius IV (1210 - 1287)
• Celestine V (Saint, 1215-1296)
• John XXII (†1245-1334)
• Callisto III (1378-1458)
The Battle of Lepanto took place on October 7, 1571 when a fleet of the Holy League decisively defeated the main fleet of the Ottoman Empire in five hours of fighting on the northern edge of the Gulf of Patras. The Holy League credited the victory to the Virgin Mary, whose intercession they had implored for victory through the use of the Rosary at the urging of Pope Pius V. He later instituted a new feast day of Our Lady of Victory to commemorate the battle, which is now celebrated by the Catholic Church as the feast of Our Lady of the Rosary. Admiral Andrea Doria had kept a copy of the miraculous image of Our Lady of Guadalupe given to him by King Philip II of Spain in his ship's state room. There was no apparition reported at this battle.
October 13, 1884, Pope Leo XIII had just finished celebrating Mass in a chapel in the Vatican. Afterwards he composed the prayer to St. Michael and later instructed that it be promulgated to the world. He claimed that he heard the voice of Satan boasting to Our Lord: “I can destroy your Church.” Our Lord responded: “You can? Then go ahead and do so.” Satan replied, “To do so, I need more time and more power.” The Lord said, “How much time? How much power?” “75 to 100 years, and a greater power over those who will give themselves over to my service.” was Satan’s reply. Our Lord said, “You have the time, you have the power. Do with them what you will.”
According to his his own testimony, Pius XII (1958) witnessed in 1950 a miracle of the sun four times, but never saw an apparition. He saw this as divine encouragement for his proclamation of the dogma of the Assumption. Apart from this, there is no modern Pope or contemporary figure in this list.
Marian apparitions to Popes are officially approved by definition as there is no higher authority to rule on their authenticity.
Laurentin, Rene and Sbalchiero, Patrick. Dictionary of the Apparitions of the Virgin Mary. 2010 Edizioni ART. pp. 562 - 563