I read a bit about him and how he was a great conquerer. But he only ever took over Asia. How far off am i in this question?
Could you reword your question a bit?
Genghis Khan could not have fought the Romans. The Western Roman Empire fell in 476, and the Byzantine Empire, the eastern half of the Roman Empire, did not really exist between 1204 (Siege and Sack of Constantinople by the Fourth Crusaders) and 1261 (the Recapture of Constantinople). By contrast, Genghis Khan ruled from 1206 to 1227.