Game Of Thrones: Is Tyrion Lannister Actually A Targaryen?
His Relationship With Tywin
Tyrion's relationship with his father at times makes that between Luke Skywalker and Darth Vader look relatively pleasant. Tywin, in both books and show, loathes his son for being a dwarf, for his whoring and drunken ways, and because his wife died giving birth to him.
There are a couple of key quotes to be referred to in particular when theorising about Tyrion not actually being Tywin, such as when he says: "...Since I cannot prove you arent mine." This could be taken that he knows Tyrion isn't his son, but has nothing to back up such a claim. Furthermore, his last words to him are actually: "You are no son of mine!" He may be speaking figuratively, or he may be using his final moments to finally unburden himself of this truth.
Tywin also constantly refuses to acknowledge Tyrion as an heir to Casterly Rock, stating he will never rule there despite that fact that neither Jaime or Cersei would be able to.
If Tywin isn't Tyrion's father, then who is? Well, at the time of Tyrion's conception, Tywin would have been Hand of the King