Maester Aemon also had a brother called Aegon, he referred to him as 'Egg' and this is talked about more in the books not exactly sure if it is noted in the T.V. show at all but the Aegon that Aemon is comparing to the wildling babe was once King of the Seven Kingdoms but is long dead at the time the show is set.
Here is a wiki page that might will give you more detail on this https://awoiaf.westeros.org/index.php/Aegon_V_Targaryen
I like this idea what makes it more interesting is that Aemon's last words to Jon were also his last words to his brother Aegon which were -
'Kill the boy and let the man be born'