No way of knowing. There are a couple of theories.
One is that the picture Illyrio has of his late wife is Aegon's mother - she does have Targ blood of the bastard line that fled after one of the Targ civil wars, can't remember offhand. Another is that she's Aegon's mother, and not a Targ at all, but has white-blonde hair and bluish/purple eyes. Either way, it's an attempt to get Illyrio's progeny on the throne.
It's also unlikely that JonCon himself knows. He was not present for the boy's entire life. JonCon fought with the Golden Company when he began in exile and only later learned of the boy. He loved Rhaegar so much that he'd believe anything.
There is a belief that Aegon is the mummer's dragon that Dany sees in the House of the Undying. Varys was a mummer, so if Aegon is his plot - along with Illyrio, then he is the mummer's dragon.
"A faceless horror of bone and brain and gore. None of us looked long. Tywin said that it was Prince Aegon and we took him at his word." Kevan Lannister
I really didn't pay that much attention to Illryio, but if what you're saying is true (Aegon is his son) why wouldn't he dispatch Viserys, announce the kid as Aegon and press Daenerys into marrying him. Why would Varys want Illyrio's blood on the throne?
I probably have to read these again.
lefty