Bloodhall Priest

Cards are discarded in a Magic game only from a player's hand. Effects that put cards into a player's graveyard from anywhere else do not cause those cards to be discarded.

If you discard a card with madness while a spell or ability is resolving, it moves immediately to exile. Continue resolving that spell or ability, noting that the card you discarded is not in your graveyard at this time. Its madness triggered ability will be placed onto the stack once that spell or ability has completely resolved.

Casting a spell with madness ignores the timing rules based on the card's card type. For example, you can cast a sorcery with madness if you discard it during an opponent's turn.