There is a lot about Melchisedec we do not know, but there is one woman that knows something about the child she carried, and that women is the mother of the Man Christ Jesus. Further more we know that Scripture, by carefully established genealogy, informs us that Joseph was indeed His father, although not begat by Joseph. There is not one scintilla of Scriptural evidence that would refute that the man Christ Jesus was not a physical descendant of David through Joseph His earthly father, in spite of Joseph not begetting Christ physically by physical intercourse with Mary.
There are two, not one, issues that concern Christ. First, he is the Eternal God and as such has no beginning of days. There is another truth as well, and that He came as a man, with a day of birth as to His physical body He chose to manifest His presence in while on this earth, having both mother and father. There is no question that He was not begat as we are, for Mary was indeed a virgin having not known a man. Just the same, Scripture tells us in two, not one lineages, that His physical lineage was that of Joseph’s. You put that together as you wish, but I will just let Scripture be as it is and accept both notions as true. Joseph did not begat Jesus but was indeed His earthly father and Mary was His earthly mother. Still yet, from His eternal perspective as God, it can be rightfully stated that He had neither mother nor father nor a beginning of days.