No, the Khazars ceased to exist as a distinct people in the Middle Ages, and there's no one today, Jewish or otherwise, who could reasonably be described as an ethnic Khazar. There was, however, a small population of Turkic-speaking Karaites (members of a minoritarian Jewish sect that rejects the rabbinic and talmudic tradition) living in Crimea; the Germans considered them sufficiently distinct that they were mostly able to avoid anti-Jewish measures.