Yes, the Khazar hypothesis has no confirmation in modern genetic studies. Maybe some fraction of Ashkenazi ancestry is from Khazars, but not any significant part - genetic studies show that Ashkenazi Jews share the same Ancient Middle Eastern ancestry, with some significant Mediterranean (most likely from conversions in Roman times) admixture, as well as smaller admixtures from other peoples (for example Slavic - mostly Polish -, German, French, etc. admixtures - occuring in post-Ancient times when Jews lived in Eastern and Central Europe), with Sephardic and other Jews.
However, what is interesting is that in the past some of Ashkenazi Jews actually did believe in significant Khazar role in their ethnogenesis.
For example Jewish pre-war physical anthropologist and race scientist (yes, these studies were popular back then - also among Jews) from Poland, Dr Henryk Szpidbaum, in his "Racial structure of Polish Jews" (chapter 34. of book
"Jews in the Reborn Poland... " published in 1933) believed that not all, but a relatively large part of Polish-Jewish ancestry were Khazar admixtures - and he described Jews with visible Khazar admixture, their anthropological type, as "Przednioazjatycki" ("Western Asiatic"). Of course at that time DNA was unknown, and physical anthropologists were classifiying people into "anthropological types" basing on their physical appearance, skull shape, etc. - believing that physical appearance is strongly correlated with genetic distance or genetic closeness between people (populations which are close to each other genetically would be described as a "race"). Modern genetic studies show that this is not really the case (that's why various Jews can look differently despite having largely common ancestry, as genetic studies show).