He is exiled to the Night's Watch for the assassination of Daenerys. Jon became the last known living member of House Targaryen and his identity as the son of Rhaegar Targaryen is kept hidden from Westeros. After she laid waste to a surrendered King's Landing, Daenerys was assassinated by Jon Snow to prevent further destruction. House Lannister replaced House Baratheon as the royal House following the destruction of the Great Sept of Baelor, but the realm was reconquered by Daenerys Targaryen, retaking the Iron Throne following the Battle of King's Landing. The two surviving Targaryens, Viserys and Daenerys, fled into exile to the Free Cities of Essos across the Narrow Sea. House Targaryen conquered and unified the realm before it was deposed during Robert's Rebellion and House Baratheon replaced it as the new royal House. House Targaryen of Dragonstone is an exiled Great House of Westeros and the former royal House of the Seven Kingdoms.
The banner of House Targaryen, the royal house of Westeros.
' Half the Targaryens went mad, didn't they? What's the saying? 'Every time a Targaryen is born the gods flip a coin.'' ― Cersei Lannister to Tyrion Lannister