Theseus's paternity seems to be in question. He seems to be a demi-god, as the son of Poseidon. But he was also the son of Aegeus.
Who was his father?
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As someone has already commented, the confusion is between Aegeus and Poseidon. This question does not have many alternate interpretations, it's just that it's never made clear, who the father of Theseus is. In Wikipedia the double paternity is addressed:
Still without a male heir, Aegeus asked the oracle at Delphi for advice. Her cryptic words were "Do not loosen the bulging mouth of the wineskin until you have reached the height of Athens, lest you die of grief." (...) This puzzling oracle forced Aegeus to visit Pittheus, king of Troezen, who was famous for his wisdom and skill at expounding oracles. Pittheus understood the prophecy and introduced Aegeus to his daughter, Aethra, when Aegeus was drunk. But following the instructions of Athena in a dream, Aethra left the sleeping Aegeus and waded across to the island of Sphairia (...) and was possessed by the sea god in the night. The mix gave Theseus a combination of divine as well as mortal characteristics in his nature;
In the Greek version of Wikipedia, it's made clear that Aethra did sleep with Aegeus at night.