Rumor has it that there would be no human father DNA.
Unfortunately, neither the Shroud of Turin, nor the Turd of Shrowin has any examinable DNA.
However, there IS the Promise reported in Matthew 18, that ANYTHING asked of the Father, in the name of Jesus, will be granted.
(Also a separate passage where it is claimed that Risen Jesus appeared to over 500 people)
So, a few Christians could gather and ask of the Father, in the name of Jesus, that Risen Jesus be allowed to appear before another crowd of "over 500 people", like, say during half time at a televised American football game, and bleed into a sterilized beaker.
This would not only answer your question, but it would prove that the Promise reported in Matthew 18 was not just some lie that some peddler of religion MADE UP about what Jesus said.
Unfortunately, in the centuries since the Bible was first formalized, no Christians have dared to even ASK.
Even though First Thessalonians instructs them to "Prove all things", and proving "Risen Jesus" is one of the most important things to prove.
Hey, Christians... why not give it a try?
What have you got to lose?