I think you may be referring to the Khazars, a Turkic tribe whose leaders did indeed convert to Judaism in the 8th century. It does not seem that even a plurality of the tribe as a whole was ever Jewish though, and by the end of the 10th century they had almost all converted to Islam instead.
I vaguely recall reading about one study which found that less than 1% of European Jews have the genetic markers which they would have if they were of descended from the Khazars or any other Turkic group. They instead share the genetic markers with other Semitic peoples like Arabs.
If the Khazars converted to Judaism that would have little effect on genetics; and the same obviously goes true with any conversion. The presence of Judaism all over Europe and in Africa, Jemen etc can't possibly be the result of emigration alone (Ethiopian Jews, for instance, are black). Already in Roman times Judaic communities could be found throughout the empire. To explain such a huge population dispersal/growth it has been assumed that Jewish birth rates were substantially higher than average (based on what? Were death rates also substantially lower?); but even assuming this does not account for the spread of Judaism over such a wide area. One might assume that this is related to the diaspora myth, which basically says that Judaism was uprooted from Israel and dispersed over the four corners of the earth. But Judaism wasn't uprooted, nor was the population of the area; there are no records to support that idea.
Basically, the idea is that the Jews of Europe weren't really descendants of the ancient Judeans, but converts (this is usually cited as an anti-Semitic theory, but there has been serious consideration of it). The Christians then told these Jews that they were the direct descendants of the exiled Judeans who had been punished for rejecting the true Messiah, but in reality there was no mass expulsion of Jews from the Levant at all.
The latter would be in accordance with several factors, such as the Assyrians deporting elites (not entire populations, if only because that would be beyond anyone's means), the Babylonian exile community was centered in Babylon (the city, not the countryside), the fact that the Jewish Wars did not lead to a mass expulsion of the local population (there are no records to this effect, instead Jerusalem being banned for a limited period of years), mass conversion of inhabitants following Islamic conquest ('mass' immigration by Arabs couldn't possibly have accounted for this, if only because Arabia did not contain any 'masses'; even today the peninsula is still thinly populated), Judaic proselytizing (which was common in ancient times). Most importantly, all through the diaspora there remained a Jewish community in Israel.
One might think of the Euopean 'peoples movements', which was accepted knowledge til at least the mid 20th century; we now know that no such 'peoples movements' occurred. Mass immigration/emigration are certainly rare in history, especially among such sedentary populations as constituted most civilizations, dependent as they were on agriculture. (A clear example can be found with the Irish who emigrated en masse to the US following potato disease-related famine. But this occurred in a time when mass transportation was available.)
On the face of it, what you seem to be describing is a Jewish/Judaic myth, rather than a Christian/antisemitic one (although there are plenty of those, to be sure).