Italian word prodigio comes from Latin pro-, Latin adagium (Proverb, adage.)

Detailed word origin of prodigio

Dictionary entry	Language	Definition
pro-	Latin (lat)	(prefixed to verbs of utterance) in place of, on behalf of. (temporally) prior, fore-. Action directed forward or in front. Advantage. Bringing into being, forth, or into the open. Downward and forward movement. Forward direction, forward movement. Prominence.
adagium	Latin (lat)	Proverb, adage.
prodigium	Latin (lat)	Omen, portent, prophetic sign. Prodigy, wonder.
prodigio	Italian (ita)	Prodigy. Wonder, marvel Prodigy (attributive).

Words with the same origin as prodigio