Faegon is Fake!
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During the time of Danaery's great great grandfather the King's "natural" son Dameon Blackfyre tried to claim rights to the iron throne, which led to a civil war in Westeros. Afterwards the Blackfyres were exiled to Essos, but they continued to try to take the Iron Throne until the last descendant was slain by Ser Barristan Selmy.
Illyrio Mopatis, the man who sheltered Danaerys in Pentos and set up her marriage to Khal Drogo had a wife who was Volantine. The Volantine share the same ancestors as the Targaryn's and have the same physical features, silver hair and purple eyes. The theory is that Aegon is his son, which makes a lot of sense when you consider his actions.
It's also theorized that Aegon is a Blackfyre, and probably so is Varys.
In Danaery's vision she saw a "mummer's" aka. fake, dragon and a stone dragon. Aegon's surrogate father, Jon Connington is infected with grey sacle, aka. the stone man disease, so he could be the stone dragon and Aegon the fake dragon.
Also Conning was the commander of the sell sword group the Golden Company, who has pledged themselves to Aegon. The Golden Company was founded by Daemon Blackfyre's brother and he other westerosi knights that followed him into exile and they continued to serve them in the rebellions. In other words the whole purpose of the group is to take back the throne for the Blackfyres.
Each morning she wakes with a dream to describe. Something lovely that bloomed in her beautiful mind. I said, I'll trade you one for two nightmares of mine.