Jews are not Khazars but they were citizens of the Kingdom of Khazaria and once ruled it. The Jewish Khazarians were immigrants, converts or descendents of those who intermarried. It's really very simple. Jewish DNA is mainly Middle Eastern but has traces of other area groups.
@BigPreme
Try Googling Khazaria DNA. There is a genetics research section in Khazaria.com. For some reason, I get an error message when I try including it here.