I would presume that, since He was manifested in the flesh (1 Tim 3:16), that flesh would have had DNA.
"His mother, Mary, provided half of the chromosomes. Who provided the other half? Was he conceived as you and I were, with the union of egg and sperm cell?"
God provided the 'other half' of Jesus' DNA. It was a miraculous conception, not a normal, biological one. Jesus had no biological father.
So, if they had performed a "paternity test" on him, what would his DNA show?