What is the evidence that Jon is a bastard targaryen? And tyrion is one too? I read the books twic e and didn't pick up on that..
ok well let me start out by saying that there is a lot of good evidence for jon being a targaryen, enough that iâm fairly convinced he is one. however, there is very little actual evidence for tyrion being a targaryen. i think there are enough little hints to warrant a discussion, and given how grrmâs been known to foreshadow things, i do accept the theory to be a possibility, even though i personally lean toward being doubtful that itâs true. also none of these are my theories, this is mostly an amalgamation of things more observant people have pointed out.
ANYWAY iâll do tyrion first because thereâs less evidence. but people think he may be a targaryen because:
there are some lines in the books that cause people to believe that aerys targaryen raped joanna lannister before tyrion was born
tyrion mentions to jon in AGOT that he was always fascinated by dragons and dreamed of them as a child, and targaryens are know to have dragon dreams (as maester aemon tells sam)
tywin shows extreme dislike toward tyrion throughout his whole life
tywin says the line âyou are not my sonâ to tyrion, which some take to be foreshadowing
tyrion is described as having white-gold hair, which many think sounds more similar to targaryen hair than jaime and cerseiâs hair, which is described to be a deep yellow-gold.
tyrionâs one eye is described as black, and there were targaryens who were known to have deep purple-black eyes
i think thatâs most of the evidence toward tyrion being a targaryen. you could probably argue against all of these points, but i think thatâs what the theory is built upon.
NOW when people speculate that jon is a targaryen, they are referring to the theory that jon is the son of rhaegar targaryen and lyanna stark. evidence supporting this is:
ned stark uses a lot of phrases like âjon is of my blood,â âjon is my familyâ etc but never calls jon his son, which suggests that jon is a stark, but not ned starkâs son.
ned was with lyanna when she died, and he remembers that the air smelled of âblood and roses.â the blood could mean she died in childbirth. blue roses were always heavily connected to lyanna, and rhaegar gave her blue roses when he crowned her queen of love and beauty at the harrenhal tourney, so if rhaegar knew lyanna was dying, he may have brought her these roses to comfort her.
lyannaâs last words were âpromise me, ned.â ned officially says this was lyanna asking ned to bury her at winterfell, but people take this to be lyanna asking ned to raise jon as nedâs bastard, and not tell anyone of his true parentage. ned remembers this quote many times throughout AGOT, so it most likely has a more urgent meaning behind it than just a place-of-burial request
 if we believe robert baratheon, we are meant to believe that rhaegar kidnapped lyanna and hid her away in a tower down south. there are several holes in this story. for one thing, rhaegar is described by everyone else in the series as being gentle and kind, loved by everyone, and generally not the type to kidnap a woman he respected and cared about enough to name queen of love and beauty. also, the kidnapping theory makes lyanna out to be a meek victim type, which she certainly wasnât. as we learned by meera reedâs story of the tourney at harrenhal, lyanna was at least a strong-willed, defensive woman, and at most the knight of the laughing tree, a veritable tourney champion in her own right. she does not seem like the victim that robert makes her out to be, which makes me think there is more to the story.Â
as we see in danyâs house of the undying vision, rhaegar targaryen fervently believed that he needed to have three children. there is evidence that elia martell could not have any more children after giving birth to two children. therefore, it is likely that rhaegar sought out lyanna (with eliaâs consent, polygamy was recognized as valid by targaryens) in order to have a third heir. in this case, it is likely that the union between rhaegar and lyanna resulted in a child
there is also the fact that lyanna disappeared with rhaegar nearly a year before she died, so just long enough to become pregnant/give birth.
lyanna died in the tower of joy (in dorne). as ned remembers, there were multiple kingsguard members there. there is really no explanation for why the kingsguard would be there unless lyanna was carrying/giving birth to rhaegarâs heir.Â
going back to the house of the undying scene, at one point dany observes a blue rose growing in a wall of ice. as i already said, blue roses are heavily connected to lyanna, and this suggests that a piece of lyanna (jon) lives at the WallÂ
ned seems to feel a lot of guilt whenever he thinks about jon, regretting the things he never told him. this suggests that jonâs mother isnât just some random woman, but instead that jonâs parentage is significant and vital information that jon needs to know.
jon is described as looking very similar to arya, and arya is described as looking exactly like lyanna. by this, we know that jon looks very similar to lyanna.
jon has at least one dream in which he is searching for something  in the winterfell crypts. lyanna is buried in the crypts, so it may be a symbol of  how there is important information regarding jonâs parentage hidden there. bran also has dreams involving jon, the three eyed crow, and the winterfell crypts.
the series is called âa song of ice and fire,â how awesome would it be if there was a character who was half stark (ice) and half targaryen (fire)?
thatâs most of the evidence i can think of. in my opinion, this evidence is pretty solid in favor of jon being the son of lyanna and rhaegar.Â
anyway i hope that helped!:)