Luke 1:36, Elizabeth your relative. While Mary was of the royal lineage of David through her father, she also was a relative on her mother’s side of Elizabeth, the priest-wife of Zacharias, who was a daughter of Aaron (Luke 1:5). In Matthew one and Luke three two different genealogies are given for Yeshua, both of which go back to King David. One is presumed to be that of Joseph and the other is that of Mary. In this way, Yeshua was a direct descendant of David legally through Joseph, his step-father, and genetically through Mary, his mother. Does this mean that Mary was of priestly as well as Davidic lineage. Yes, but not patrilineally, only matrilineally. In the Scriptures, tribal lineage was determined through the father’s family line and not the mother’s.
In the case of Mary and Elizabeth, they would have shared common grandparents making them cousins. Their grandfather would have been a priest. In the case of Elizabeth, her father—the son of her priestly grandfather—would have carried the priestly line making her a daughter of Aaron (Luke 1:5). In the case of Mary, her mother would have been her priestly grandfather’s daughter meaning that she was of priestly lineage, but not her children, unless she married a priest.
It seems that Yeshua would have carried priestly blood in his genes, but he was legally a priest through patrilineal descent. To be sure, Yeshua was a priest, but not one of Aaronic lineage, but after the order of Melchizedek, which was the priesthood of the firstborn son passed on generationally. Yeshua was the first born son of Elohim eternally, which is why he is presently at the right hand of Elohim acting as our Great High Priest (Heb 1:3 cp. 3:1; 4:4; 8:1).
Therefore, Mary laid claim to a Davidic as well as a priestly lineage (Jesus the Messiah, by Edersheim, p. 105). This means that Yeshua was not only of direct Davidic lineage, but was of priestly lineage as well.