Yes, Jon Snow is a Targaryen. However, it is worthy to note that this information was not revealed in the early seasons of Game of Thrones. During the beginning of the series, it was said that Jon Snow was Eddard “Ned” Stark’s bastard son. However, in the finale episode of the seventh season of Game of Thrones, Bran Stark revealed that Rhaeger Targaryen and Lyanna Stark were in fact in love with each other.
They secretly got married and Lyanna conceived a child. Lyanna then asked Ned to keep Jon safe, so Ned made everyone believe that Jon Snow was his bastard son. Now that the truth is out, Jon Snow is the legitimate heir to the iron throne because he is Aegon Targaryen.
