You are of course refering here to the stepfather of Jesus whose genealogy is recorded in Matthew, and he is Joseph the son of Jacob of the tribe of Judah, having descended through Solomon.
He, who was the father of Marys second born child 'Joseph' of whom we know so little, did not have any sexual relations with Mary until after she had given birth to the first of her three biological sons, I believe that everyone knows that this Joseph is not the biological father of Jesus.
The Joseph that I am refering to is the Joseph that is mentioned in the genealogy of Jesus, the one who is the biological father of Jesus and the half brother to Mary the daughter of Heli who is a Levite and is descended through Nathan the priest who was the half brother to Solomon and stepson and son-in-law of King David.
Nathan, was the biological son of Uriah the Hittite who had married into the tribe of Levi, having married Bathsheba the daughter of Ammiel the son of Obed-Edom who was a descendant of Moses the Levite through his second wife who was the daughter of Hobab the second father-in-law to Moses whose grandson Jonathan, was taken to the land of the North by the Danites: of whom none are mentioned among the 144000 chosen ones who are chosen from the 12 tribes named after 12 of the 13 children of Jacob.
This Joseph, who was a Levite from Cyprus, apparently met Mary while she was visiting their cousin Elizabeth, where many members of the family had gathered to rejoice with the old woman. It is there that Mary who, until then had been a virgin, was to fall pregnant, which conception was concealed beneath the wings of the Lord of spirits which had overshadowed the righteous act in obedience to the Holy Spirit. It is very unlikely that Mary knew at that time that this Joseph had been sired by her father. From Young's Analytical Concordance to the bible, "Almah":...Concealment...unmarried female.
This Joseph who was the half brother to Mary who had adopted John whom Jesus had surnamed 'Son of Thunder, took his sister and John who was surnamed "Mark" which means "Hammer" up north into the land of Pamphillia, where in the town of Ephesus, the grave sites of Mary and John can still be visited today.