the crow flying
the crow flying asked Rick Riordan:

If a demigod took a DNA test? what would the result look like? Would the mist make it a faulty test or would they have such a wild family tree that the company would consider it a glitch?

Rick Riordan It would probably come back as a faulty test, but I'm just guessing. Since gods don't have blood, but rather golden ichor in their veins, it seemed reasonable to assume they also didn't have DNA. Like so many things godly and mythological, it can't be explained or understood in human terms. At some point, you just have to say, "It's magic!"
Rick Riordan
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