The first Khazarian ancient DNA paper has been published in here. The paper was written by Dr.Anatole A. Klyosov and Dr. Tatiana Faleeva and appeared in Advances in Anthropology, an online journal that Klyosov is its chief editor. From my familiarity with Dr. Klyosov, his papers are going through a peer review process prior to publication. It is nonetheless a shame that a paper covering such an important topic did not appear in a more mainstream journal where more people would be able to evaluate its finding. My impression was that much more data/information could have been included in the paper.
Briefly, the authors sequenced parts of the Y chromosome of 2 Khazars. Looking at the haplogroups and STR markers the authors found no resemblance to “typical” haplogroups and STR markers that appear among Jews, as far as the authors know. In other words, the authors did not search in any specific database, this is based on their own experience. The paper also does not allow a proper evaluation of the methodology and is open to speculation about the meaning of the results.Many people, myself included, have been waiting for this day for a very long time and I can only hope that this is only the first of many papers dedicated to study Khazarian ancient DNA.
Abstract
To understand a biological tribal affiliation (in terms of Y-chromosomal haplogroups, subclades, and haplotypes) of two excavated Khazar bone remains in the lower Don region in the south of Russia, we have extracted and analyzed their DNA and showed that both belonged to haplogroup R1a and its subclade Z93. The pattern could be considered typically “Turkic”, and not a Jewish DNA lineage. Their haplotypes were also identified and reported here. The haplotypes indicate that both Khazars were unrelated to each other in a sense that their common ancestor lived as long as 1500 – 2500 years earlier than them, in the middle of the II millennium BC—beginning of the I millennium BC, during typically Scythian times or somewhat earlier. Their haplotypes are unrelated to well-known Jewish haplotypes of haplogroup R1a
The DNA Project 
So does this prove the the Israeli people in Israel are descendents of ancient Israelite and not Khazarians or Turks?
Two ancient Khazar skeletons and their haplogroups proves nothing.
Extremely tiny sample size.
Would a burial of 2 Ashkenazi Jews with western European haplorgoups of R1b prove Ashkenazi Jews are from western Europe?
This is a very small sample size of people known to be heterogeneous so we cannot make any robust conclusions. Without knowing which people share the haplogroups of these ancient samples, there is not much to say beyond what I wrote.