The difficulty with this question is the enormous timespan of the many various Jewish diasporas in history. With the very first one taking place in the samarian kingdom in 733 BCE by the Assyrian empire. When the first temple was destroyed by the Babylonians and the Judean kingdom ended, most Jews were exiled to Babylonia and what eventually became the Persian empire. After Cyrus ordered the temples rebuilt many if not most Jews remained in Persia and ended up as far away as India, and according to the Talmud even in the city of Wurms in Germany. But most remained in the middle east. After the destruction of the second temple by the Romans, "Tacitus declares that Jerusalem at its fall contained 600,000 persons; Josephus, that there were as many as 1,100,000, of whom 97,000 were sold as slaves". This marks what's really considered today to be the start of the Diaspora. The communities in the middle east, levant and north Africa, became known as the Sephardi and Mizrachi communities. Sephard being the Hebrew word for Spain as many Jews in Spain after the expulsion migrated to North African and Egyptian communities. Also, much smaller communities were found all along the silk road and even in China(hence the famous synagogue at Kaifeng). The communities in the Muslim world would last until the establishment of the state of Israel in 1948, at which point they were expelled. according to the Jewish encyclopedia of 1906 the world population of jews broke down thus
so we can see that if we include Asia Africa and the in the middle east we come out to about 1.5 million in 1900. of course, the accuracy of these numbers is called into question as getting accurate figures for Asia and the middle east at the time was tricky.
If you're American, you've mostly heard of European Jews because that's the majority Jewish population who moved to America. But in truth there are many Jewish communities from many places.
In terms of directly east, there were huge Jewish communities in Syria, Iraq, and Iran (which are all East of Israel). The Syrian and Iraqi communities moved en masse to Israel in the late 40s/early 50s, and the Iranian community did so more gradually in the 70s (there is still a small community in Iran today). These communities have been there since ancient times--not just the result of diasporas, but simply migration over time. These communities existed even in the biblical era, and were well established in the second temple period. In case you're unaware, there was also a large Jewish community in North Africa and Yemen, both of which basically all moved to Israel (with a few outposts remaining in Tunisia and Morocco). Also Ethiopia, which effectively all migrated to Israel in the 90s.
In terms of further east, there are Jewish community outposts in India and China. China has the Kaifeng Jews, a small isolated community whose origin is somewhat unclear--probably established by traders who came along the silk road. There are also Jewish communities in central Asia ("Bukharians"), though many European Jews migrated there during the Soviet era too. Central Asian Jewish communities mostly moved to Israel or America in the late 20th century for the most part.
India is a bit more interesting--a few cities had/have Jewish communities from ancient times (though when exactly is an open question). A lot of the population were Iraqi Jews who moved there relatively recently (18th-19th century), though.
This is a brief survey of who was where, more detailed info about all these communities a bigger project than one could do on reddit probably.