According to Online Etymology Dictionary (www.etymonline.com)
“Prodigal” originates from the Latin “prodigus”=wasteful
“Prodigy” originates from the Latin “prodigium”=prophetic sign, omen, portent, prodigy
Whether or not “prodigus” and “prodigium” are related, I think we need someone who is proficient in Latin to tell us. They do seem similar, but so do “rain” and “ruin”.