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”.

Both words are of Latin origin, but as far as I know that is the full extent of their connection. Sometimes words are just very similar and in those cases you unfortunately just have to make mistakes and learn the differences through trial and error and memorization.