Genghis Khan was the founder and emperor of the Mongol Empire around the year 1200. John of Montecorvino (1247–1328) an Italian Franciscan missionary was said to be possibly the first person to translate the New Testament and Psalms into Mongolian.
Therefore we can basically assume the New Testament was the Catholic New Testament (which is the same as the Protestant one):
-The Gospels according to Matthew, Mark, Luke and John
-The Acts of the Apostles
-The Letters of St. Paul to the Romans, 1 and 2 Corinthians, Galatians, Ephesians, Philippians, Colossians, 1 and 2 Thessalonians, 1 and 2 Timothy, Titus, and Philemon
-The Letter to the Hebrews, the Letters of James, 1 and 2 Peter, 1, 2 and 3 John, and Jude
Since poor Genghis died around 1227, he probably never got a chance to read it himself.
Yet the Catholic history does not reach the full answer because although Catholic missionaries may have been the first to translate a full New Testament into Mongolian, there were not the first Christian missionaries into the region.
This article says:
Nestorianism was the first form of Christianity to be proselytized among the Mongols, in the 7th century, and several Mongol tribes became primarily Christian. During the rise of the Mongol Empire in the 13th century, the Great Khans, though mostly Shamanists and Buddhist, were religiously tolerant towards the Nestorian Christians, Muslims, and Manichaeans. Many of the khans had Nestorian Christian wives from the Kerait clan, who were extremely influential in the Mongol court. During the rule of Mongke Khan, Christianity was the primary religious influence. After the breakup of the Mongol Empire in the 14th century, Nestorian Christianity nearly disappeared from the region.
Nestorianism was an Eastern sect considered by the West as Heresy for its unique view of the nature of Christ as being two distinct persons.
According to this article, the Nestorian Canon "excludes the New Testament books of Revelation, Jude, Second John, Third John and Second Peter, because the use of those books was not attested in the churches of Persia early enough to have been woven into the canonical tradition. "