The Nestorian branch of Christianity was the first major schism, as far as I know. Due to being declared heretics by after the Council of Ephesus, Nestorians were generally persecuted in and eventually pretty much disappeared from areas held by the (eastern) Roman Empire. However, they were less persecuted than other Christian sects in Zoroastrian Persia, where Christians were generally suspected of being Roman catspaws which these people, who were deemed heretics by the Romans, were less likely to be.
The Nestorians also attempted to proselytize areas north and east of Persia and had some early success among the Turkic people in Modern-day Uzbekistan and Turkmenistan. However, after the Muslim conquest of Persia, they were largely marginalized by the spread of Islam.
The POD would involve a more successful conversion of peoples between the Caspian Sea and the Himalayas, sufficiently so that they are not subsequently converted by the Muslims. Perhaps there is more of a focus on converting the Turkic peoples to try and start up a Nestorian nation and thus less effort spent on trying to convert India and Tibet. Perhaps there are simply some lucky breaks instead. Perhaps Nestorian faith copies some elements of Zoroastrianism (which people living next to Persia would at least be aware of) due to the fairly amicable relationships between the clergies and the fact that Zoroastrian priests becoming Nestorian was not uncommon.
How would this affect the steppe nomads of Central Asia? What would the relationship between the Nestorians and the Byzantines eventually be like?