Then how can it be a race if no GÇ£Jewish ancestryGÇ¥ is needed to be considered one? Or are there religion-Jews and race-Jews ?

Jewish descent is Matrilineal not Patrilineal. It may show that the males are of middle eastern and jewish descent but their children are not.

Before 2006, geneticists largely attributed the genesis of most of the world's Jewish populations, including Ashkenazi Jews, to founding effects by males who migrated from the Middle East and "by the women from each local population whom they took as wives and converted to Judaism." In line with this model of origin, David Goldstein, now of Duke University, reported in 2002 that, unlike male lineages, the female lineages in Ashkenazi Jewish communities "did not seem to be Middle Eastern", and that each community had its own genetic pattern and even that "in some cases the mitochondrial DNA was closely related to that of the host community." In his view this suggested "that Jewish men had arrived from the Middle East, taken wives from the host population and converted them to Judaism, after which there was no further intermarriage with non-Jews."[46]
However, a 2006 study by Behar et al.,[1] based on high-resolution analysis of haplogroup K(mtDNA), suggested that about 40% of the current Ashkenazi population is descended matrilineally from just four women, or "founder lineages", that were "likely from a Hebrew/Levantine mtDNA pool" originating in the Middle East in the 1st and 2nd centuries CE. Although Haplogroup K is common throughout western Eurasia, "the observed global pattern of distribution renders very unlikely the possibility that the four aforementioned founder lineages entered the Ashkenazi mtDNA pool via gene flow from a European host population:
"..Both the extent and location of the maternal ancestral deme from which the Ashkenazi Jewry arose remain obscure. Here, using complete sequences of the maternally inherited mitochondrial DNA (mtDNA), we show that close to one-half of Ashkenazi Jews, estimated at 8,000,000 people, can be traced back to only four women carrying distinct mtDNAs that are virtually absent in other populations, with the important exception of low frequencies among non-Ashkenazi Jews. We conclude that four founding mtDNAs, likely of Near Eastern ancestry, underwent major expansion(s) in Europe within the past millennium.."[1][46]
In addition, Behar et al. have suggested that the rest of Ashkenazi mtDNA is originated from ~150 women, most of those likely of Middle Eastern origin.[1] However, other studies by Behar indicate that this mtDNA is different from other Jewish populations found outside of Europe, leaving the possibility of a separate origin or even a European origin a distinct possibility