Is Tyrion Lannister a Targaryen?

One of the many questions that is haunting me is whether Tyrion Lannister a Targaryen or not?We do all know that everyone in his family hates him except Jaime Lannister.It is just because he killed his mom during his birth or something else.I remember Tywin Lannister said something about his origin and whether Tyrion is his son or not.I also read something about his mother is very much liked by the "Mad king"Aerys Targaryen.There is also an episode that Tyrion got near the two dragons in the catacombs and didn't get toast and successfully got to free the two dragons.The history tells always something about three dragon and three riders,is Tyrion actually one of the Targaryen?and now that he sided himself with Daenerys and works as the Hand of the Queen,raises more suspicions.The other Targaryen that is obviously out there is Jon Snow,we will talk about him in some other time,that's it for now comment down for your opinions on this one thanks.