Y'shua still had the DNA of his mother Miriam.
But High Priest under the order of Melchizedek
Ge. 14:18 Then Melchizedek king of Salem [That is, Jerusalem] brought out bread and wine. He was priest of God Most High,
b'shem Y'shua
Jesus would have had Mary's DNA, and not Joseph's. Joseph was of the line of David -- there is no evidence that Mary was. In fact, there is some evidence that Mary came from a Levitical family. Her sister was married to a priest.
The genealogy in Luke 3 would seem to be of Joseph's bloodline, while that in Matthew 1 records in chronological order those who inherited the royal office (passing, for example, from uncle to nephew when the uncle was without heirs).