In 1223, the Mongols invaded the lands of the Kievan Rus. In our timeline, they migrated north, eventually founding the Grand Duchy of Moscow. But what if they’d gone south?
Eastern Slavs (speaking a language ancestral to modern Russian, Belarussian, and Ukrainian) would have found the Balkans inhabited by southern-Slavic-speaking Bulgarians and Serbians, both autonomous after the conquest of the Byzantine Empire by the Fourth Crusade, and both adhering to the same brand of Eastern Orthodox Christianity as the Kievan refugees. By the time the Greek-speaking Byzantines kicked out the Latins, they would find a larger, more powerful state to the north, pushing up against Hungary to the west and the Mongol successors like the Nogai to the east.
Whether the Southern/Eastern Slavs would have remained united is another question. If not, and perhaps even if so, their states would have fallen to the Ottoman Empire. We might at most end up with a Slavic- rather than Romance-speaking country north of the Danube.
The biggest changes would occur in the North, where no Grand Duchy of Muscovy forms. Instead, Northern Slavs speaking a language related to Polish, German-speakers, Baltic-speakers, and Finno-Ugric speakers would compete with Turkic-speakers like the Kipchaks. We’d probably get lots of little principalities, perhaps coalescing in the 1500s into something like Great Lithuania in the west and a federation of Christianized Kipchaks or Tatars in the East. In the 16oos, these people would be well placed to begin eastward empire-building.