Jews have been widely distributed for thousands of years. Therefore, any single group of Jewish descent cannot in itself tell us much about the genetic composition of Ancient Jews (*)
Previously, I had suggested that the presence of Y-haplogroups Q,R1a in Ashkenazi Jews may have been introduced by a Turkic population in Eastern Europe, and hence was not present in Ancient Jews.
A recent study on Samaritans , a group which split from Jews in BC times, indicates that these belong wholly to haplogroup J, with the exception of the Cohen Samaritans who belong to haplogroup E3b. But, since Cohens in general belong to haplogroup J (which contains the Cohen Modal Haplotype), the E3b Samaritan Cohen is probably the result of some (possibly ancient) admixture event.
The Lemba of Southern Africa are physically Negroid, but the presence in their gene pool of the Cohen Modal Haplotype indicates that they are of Jewish origin. They possess 2.9% of haplogroup E3b, which however may have been introduced by other populations of Africa.
The Bene Israel of India also have traditions of Jewish descent, and they also have a high frequency of the Cohen Modal Haplotype, substantiating these claims. They lack haplogroup E3b, and the authors of the linked study suggest that they split from other Jews before E3b entered the Jewish gene pool.
The Cohens themselves have patrilineal descent, therefore they ought to represent in principle a more "pristine" gene pool of Jewish origin than other Jews who only have (almost always) matrilineal Jewish descent. They only have 1.5% of haplogroup E, in contrast to about 18% in lay Jews.
In conclusion, it's probable that ancestral Jewish groups lacked at some stage haplogroup E3b. If this turns out to be the case, then by additionally subtracting the possible Turkic/Slavic admixture (Q+R1a), as well as other clades of possible (Indo-)European origin, it appears that the ancestral Jews belonged primarily (**) to clades of haplogroup J.
(*) By Ancient Jews, I mean "as ancient as can be determined". Ethnic groups are not static entities, and undergo continuous processes of admixture.
(**) Primarily, or even exclusively at the most ancient stage.