When Dany returned to Dragonstone in "Eastwatch" after roasting Lannisters in the previous episode, Jon was there to meet her and Drogon as they landed. Instead of harming Jon, however, Drogon seemed quite taken with him — almost as though he knew something Jon didn't. Does Drogon know Jon Snow is a Targaryen on Game of Thrones?
Drogon's apparent fondness for Jon definitely seemed like a nod towards his Targaryen ancestry, though at this point only the viewers know enough about that to catch on. Both Jon and Dany were uncertain when Drogon turned his attention towards Jon, fearful of what could quickly become a fiery end to the King in the North. But instead of that, Jon acted out a scene from How to Train Your Dragon: He took off his glove and gave Drogon a nice pat on the nose like you would to a big friendly puppy you ran into on the street.
It could be possible that Drogon trusted Jon because of his Targaryen blood, even though Jon himself is still unaware of who his true parents are. In the Season 6 finale, it was revealed that Jon was the secret child of Lyanna Stark and Rhaegar Targaryen, Dany's oldest brother. Fans have been waiting for Jon to find out the truth of his parentage, and Drogon could have just given him a big tip.
The trouble is, it's not a connection Jon would be able to make on his own. No one but Bran knows that Lyanna and Rhaegar had a child, let alone that the child is Jon. Without a helpful rundown from his younger brother-cousin, Jon is going to remain in the dark about where he came from. And even though Drogon's trust of Jon is likely a wink to the audience about his father, the dragons have been shown to trust people before. In fact, they showed a similar appreciation for Tyrion, and he isn't a Targaryen. Right?
Tyrion isn't, as far as fans know, but it is a popular theory that he's the bastard son of Aerys Targaryen, Dany's father. In the books, Tyrion dreams of dragons and shares the Targaryen's telltale pale blonde hair, plus Aerys had an inappropriate fixation with Tyrion's mother Joanna. Many have speculated that that could indicate Tyrion is a Targaryen, and Dany's dragons reacting positively to him was only more proof.
However, Targaryen blood might not have anything to do with it. It's possible that the dragons are just flawless judges of character.