There is no evidence or indication in the “A Song of Ice and Fire” book series by George R.R. Martin or in the “Game of Thrones” television show that Jaqen H’ghar, a mysterious character from the Free City of Braavos, is a Targaryen. In fact, based on the available information, it is highly unlikely that Jaqen H’ghar has any affiliation with House Targaryen.

House Targaryen is a prominent family in the fictional world of Westeros, known for their distinctive silver hair and purple eyes. They are descendants of the Valyrians, who were known for their dragonlord heritage and mastery of dragonriding. Daenerys Targaryen, one of the main characters in the series, is a member of House Targaryen and is known for her silver-blonde hair and violet eyes.
On the other hand, Jaqen H’ghar is a member of the Faceless Men, a secretive and enigmatic organization of assassins from the Free City of Braavos. The Faceless Men are known for their ability to change their appearance and assume different identities, making them masters of disguise. Jaqen H’ghar is one of the many names used by this character, and it is not his real name.
Jaqen H’ghar first appears in the “A Song of Ice and Fire” series as a prisoner traveling with Yoren, a Night’s Watch recruiter, and other prisoners who are being transported to the Wall. He helps Arya Stark, one of the main protagonists, and becomes her ally and mentor. Jaqen H’ghar teaches Arya about the ways of the Faceless Men and helps her develop her skills in the art of assassination.
There is no indication or hint in the books or the television show that Jaqen H’ghar has any connection to House Targaryen. His appearance, abilities, and actions do not resemble those of the Targaryens. He has dark hair and is able to change his face at will, which is not a characteristic of the Targaryens’ distinct appearance with silver hair and purple eyes. Furthermore, the Faceless Men are known for their neutrality and do not involve themselves in the politics or conflicts of the Seven Kingdoms, including the Targaryen family’s quest to reclaim the Iron Throne.
Moreover, the Targaryens are a family of dragonlords who are known for their bond with dragons, whereas Jaqen H’ghar has no connection to dragons or any indication of possessing the blood of the dragon, which is a key characteristic of House Targaryen. In fact, Jaqen H’ghar is known for his skill in assassination, not for his ability to ride dragons or control them.
In conclusion, based on the available information from the “A Song of Ice and Fire” series and the “Game of Thrones” television show, there is no evidence to suggest that Jaqen H’ghar is a Targaryen. He is a member of the Faceless Men, a secretive group of assassins from Braavos, and there is no indication of any connection to House Targaryen in his appearance, abilities, or actions. Therefore, the theory that Jaqen H’ghar is a Targaryen is highly unlikely and lacks any substantial evidence.