魔術師の帽子 [majutsushi no boushi] or 'mage's hat' in Japanese. Not to be confused with Wizard's Hat.
Final Fantasy IX
Stats: MDEF +14, MAG +1, enhance Holy and Dark attacks
Equip: Zidane, Vivi, Garnet (Dagger), Quina, Eiko, Amarant
Abilities: Fira, Loudmouth
Buy: 600 gil (sell: 300 gil)
Shop: Cleyra (Burmecian soldier Dan's shop), Lindblum (Dragoos' shop (disc 2), Dragon's Gate merchant (disc 2)), Black Mage Village (equipment shop (disc 3)), Daguerreo (weapon shop (disc 4))
Description: Hat that holds magic powers
Type: Hat
Final Fantasy XII
Stats: MDEF 21, MP +10, MAG +5
Buy: 2,500 gil (sell: 1,250 gil)
Pictlogica

Stats (lv1): INT +15, MDEF +20
Buy: - (sell: ? gil)
Obtain: event quest Treasure Excavation, 14th Exa Battlia (Chocobo II)
Type: Accessory, Rarity: ★★★★, Element: -
Category: Equipment