From the Lord's Prayer: "Give us this day our daily bread" (Matthew 6:11, web address 1, also Luke 11.3). Chantraine mentions these passages in his review. On ou)si/a, see omicron 961.
The derivation and meaning of the adjective e)piou/sios is uncertain, and was debated already by the Church Fathers. The gloss here agrees with Origen's interpretation (PG 11.509c), making the word refer to the bread (in its spiritual sense, as used by Jesus) that is "for" (e)pi/) our true, spiritual being, essence or nature (ou)si/a). John Chrysostom also relates it to ou)si/a, but takes e)pi/ in its use as "over", thus "supernatural" (as in the Vulgate Latin translation of Matthew 6:11 supersubstantialem): PG 3.30e. Alternatively, Chrysostom and others derive the adjective instead from ei)=mi "go", so that it would mean "for the coming time, for the future". This may be interpreted either in reference to the life to come, or simply to the next day (Latin quotidianus, cf. the version of the Lord's Prayer at Luke 11:3). There can be no doubt that the word is a coinage, attempting to express some aspect of Jesus' teachings about spiritual bread. See Lampe s.v., and Foerster's exhaustive analysis in Kittel of the possible etymologies and explanations.