Something like that would be of limited relevance to the general public, but for figures involved would be a great way to get reality shows, take advantage of it with religion (although Muhammad's descendents don't seem to have gained much through this, probably since there's so many of them), or just makes tons of appearances on the History Channel and shit.
Descent from Antiquity is a major subject in historical geneology, but few lines have been found. For instance, look at Confucius's descendents who are still very important in modern China and at one point had a faction attempting to appoint them Emperor of China.
Maybe monarchs claiming to be Jesus's offspring.
You'd need Catharism or a Gnostic doctrine which holds Jesus to have married and have had descendents. If you deny the doctrine of Mary's perpetual virginity (as some Protestants do, and something you can introduce), you can get descendents of Jesus's brothers (half-brothers if you believe Jesus's true father isn't Joseph but God himself) which would also be descendents of King David.
They all claim descent from Adam and Eve, and thereby God.
So how is this any different?
There's none of Jesus's DNA around as a comparator, anyway!
Not true, Adam and Eve are not descendents of God. Adam is just dirt God breathed "life" into and Eve is just Adam's rib formed into a human being.
Quite a lot of Arabs are descendants of Mohammed including the ex-Kings of Tunis. It didn't stop them being deposed back in the fifties.
The whole "Holy Blood, Holy Grail" thing always struck me as illogical. Either (i) Jesus Christ was Divine exactly according to the Christian Scriptures -in which case "Priest after the order of Melchezidek" etc. and no descendants; (ii) Jesus Christ was Divine or Divinely inspired though not exactly according to the Christian Scriptures as we know them today - in which case any descendants would be purely human as God is not inspiring or indwelling -illustrious ancestry but nothing special in themselves; (iii) Jesus Christ was not divine and left no descendants; or (iv) Jesus Christ was not divine and left descendants- again,illustrious ancestry but nothing special. If He had left descendants who could also raise the dead and walk on water we would have noticed I imagine.
The Tolomei family of Rome claim descent from the Ptolomeys, so I understand.
That's where you get the Arian controversy and the idea where Jesus can be both Divine and a mortal man. The idea of Jesus and his wife (Mary Magdalene, Martha?) producing demigods is thus unfounded, since their father would be Jesus the mortal man instead of Jesus the Son of God. I don't think it's too unlikely the historical Jesus (who isn't the Biblical Jesus) married (IIRC a Jewish teacher would not be taken seriously if he weren't 30 years old--Jesus was 30 when he began his ministry--and if he weren't married), but he likely left no descendents or else they would have been far more important in the early church. Maybe a son of Jesus is one of the Seventy Apostles? In any case, there's no evidence for this. Prominent descendents of Jesus would decisively shift Christological disputes toward Arianism and similar beliefs where Jesus has two natures, since none of Jesus's descendents are demigods (or are they, considering the amount of miracles attributed to various saints?)