When Mehmed the Conqueror earned his nickname by conquering Constantinople in 1453, he also took another title: Caesar (Kaysar-i Rum, in Persian). Although today we think of 1453 as the end of the Roman Empire (and, to be fair, later Ottomans certainly thought of it that way as well), at the time Mehmed very much identified as simply the new Roman Emperor. The Ottomans were always happy to add a new royal title, in part because they had a hard time making the ideological case for their own reign. They clearly weren’t caliphs, and even later when they assumed that title it’s not at all clear that anybody really bought it. They couldn’t trace their descent from Genghis Khan or Timur, the two great conquerors of the age. They didn’t have a spiritual claim to power like the Safavids would later assume. And until they captured Constantinople they didn’t even have a particularly impressive capital. They just kind of were, a fact of life in a sense; but “we’re in charge because we say so,” or (for the religiously-minded) “don’t look at us, God must want it this way,” hadn’t worked as legitimizing principles for the Umayyads and they wouldn’t work for the Ottomans for very long. They worked for the Mongols during the height of their conquests, but soon after “descent from Genghis Khan” became their great marker of legitimacy.
So an Ottoman Sultan who conquered Constantinople would naturally be inclined to anoint himself the new Roman Emperor. Mehmed seems to have taken his new title seriously enough that he had designs not just on ruling the Roman Empire as it was in 1453 (which, frankly, wasn’t all that impressive anymore, just Constantinople and a little surrounding territory), but on putting the entire OG empire back together. And if you’re putting the Roman Empire back together, what better place to start than the city of Rome itself? Hence in 1480 the Ottomans invaded southern Italy with a plan to march north and seize Rome. Mehmed didn’t just want the “new Rome,” Constantinople; he wanted the old, actual Rome as well.
The landing point for the Ottoman invasion force, commanded by a former Grand Vizier named Gedik Ahmed Pasha, was Otranto, in Italy’s “heel.” This was actually a two-pronged offensive; another army besieged the Knights Hospitaller on the island of Rhodes from May through July, 1480, but ultimately failed to capture the island and had to withdraw. This Ottoman force landed and besieged Otranto on July 28. They offered the defenders clemency if they surrendered, but the Otrantan militia vowed to resist, so the siege was on. The Ottomans were able to breach the walls on August 11 and the city was lost, but those mere couple of weeks delayed the Ottoman offensive and gave Naples, the first major city to Otranto’s north, time to organize its defenses.
Things get a little murky at this point. In the aftermath of the battle, the Ottomans were said to have rounded up the remaining men in Otranto, which turned out to be roughly 800. These men were offered the choice of conversion to Islam or death, at which point one of the 800, a man named Antonio Primaldo, is said to have declared that he would die for Christ just as Christ had died for him. This was enough to win the whole group over to the idea of martyrdom, and so they were all executed. The 800 martyrs were beatified in 1771 and were canonized only very recently, by Pope Francis in 2013. They were reportedly executed on August 14, which the Catholic Church designates as their feast day, and they are considered the patrons and protectors of Otranto.
The reason I say things get murky is because, while thousands of people died during and right after the siege of Otranto, it’s not clear that these particular 800 men were killed for any special reason like resistance to conversion. “Convert or die” wasn’t typical practice for the Ottomans, who had countless Christian subjects living under their rule and were perfectly fine with that, particularly insofar as they could tax Christians at higher rates than Muslims and conscript Christian boys for their devşirme slave program (from which they drew “recruits” for the Janissaries). These 800 men may have been ordered to convert or die, but on the other hand they may have been singled out for execution as punishment for the city’s resistance and not been given the option of conversion, or they may not have been singled out at all. As best as historians can figure, contemporary Christian sources don’t say anything about a mass martyrdom at Otranto, though that could be explained by the fact that Christians wouldn’t have learned of the martyrdom until after the Ottomans were forced to leave the city. None of this changes the fact that these men were killed at Otranto, but we simply can’t be sure that they were actually martyred by the strictest religious definition of the term (which should not take away from their sacrifice in my view, but your mileage may vary).
Mehmed’s invasion of Italy fizzled out when Mehmed, personally, did. Gedik Ahmed Pasha tried to press north but met stiff resistance, and as winter was approaching he elected to leave a small garrison in Otranto and take the bulk of his army back to secure, well-supplied Ottoman territory in Albania. Meanwhile Pope Sixtus IV (d. 1484), understandably freaked out by the presence of Ottoman soldiers on the Italian peninsula, called for a Crusade. An army was formed, primarily of Neapolitan soldiers with support from Hungary, and in May 1481 they besieged Otranto. The Ottoman garrison held out, but was expecting Gedik Ahmed Pasha to return with reinforcements, and any plans to do that were scrapped when Mehmed died on May 3. He was only 49 and was probably poisoned, either by a Venetian agent or by his physician, possibly on behalf of Mehmed’s son and successor, Bayezid II (d. 1512, shortly after being forced to abdicate by his son Selim). Gedik Ahmed Pasha had to hightail it back to Istanbul; Bayezid and his brother Cem were disputing succession, and Gedik Ahmed Pasha wanted to support Bayezid (which won him nothing, as Bayezid eventually had him executed anyway, in 1482). The Ottoman garrison at Otranto, when it became clear that no reinforcements were coming, negotiated the surrender of the city and fled Italy for Albania. The Ottomans would never seriously threaten Italy again.