The three-headed-dragon theory states that three Targaryen descendants will rule the dragons. The first is Daenerys. The second depends on the theory that Jon Snow is really a Targaryen. So who's the third?
Many fans believe that Tyrion Lannister (Peter Dinklage) completes the trio. According to their thinking, Tyrion was the product of an affair between the Mad King and Tywin’s wife, Joanna Lannister.
For proof, they look to Tyrion's phsyical differences, beyond the dwarfism, from the other Lannisters. Also, things that were said by his father that could sound like a man denying his dwarf son in embarrassment, but can also be seen as that of a man who knows that he didn't father Tyrion.
For example, Tywin (Charles Dance) denies Tyrion the inheritance of Casterly Rock, saying: “Men's laws give you the right to bear my name and display my colors since I cannot prove that you are not mine.”
And then just before Tyrion kills him, the dying man’s final words are, “You are no son of mine.”
Source: Inquisitr.com