where did they come from? were they khozari or no ? what is the territory they started to live in the 3rd century?

ב"ה Shalom, This is a question of historical nature, which is meant for historians and therefore it is best to seek the experts in this field. Although, I personally have studied and researched Jewish history, this period is not my area of expertise and therefore I will suffice by saying only that there is such a hypothesis which is supported by some scholars, while others feel that this is not corroborated by historical sources. All the best