From the Super Mario Wiki
A White Magikoopa is a Magikoopa that appears in Paper Mario and Paper Mario: The Thousand-Year Door. Their name is abbreviated as W Magikoopa (no period) in Paper Mario and W. Magikoopa (with period) in The Thousand-Year Door. Like most Magikoopas, White Magikoopas can shoot magical blasts at enemies, but their specialty is healing either themselves or their allies in battle. They will sometimes ride a broom in battle, which will allow them to hover above the ground and cause hammer attacks to miss. Like all Magikoopas, they will duplicate themselves or run away if alone in battle.
In Mario & Luigi: Dream Team, Kamek creates a white-robed clone of himself called Kamek (White) to assist him in his third battle against the Mario Bros. in Dreamy Neo Bowser Castle. This clone heals Kamek, his other clones (Green and Red) and itself just like White Magikoopas.
White Magikoopas appear in Mario & Luigi: Superstar Saga + Bowser's Minions after being absent in the original game. They are labeled as Magikoopa (White). They appear as enemies and recruitable allies exclusively in Minion Quest: The Search for Bowser. They are ranged troops, and can use their magic wands to raise the unit's speed. Like other Magikoopas, they are weak against Bowser Jr.. They also reappear in Mario & Luigi: Bowser's Inside Story + Bowser Jr.'s Journey as enemies and allies in the Bowser Jr.'s Journey mode. In this game, they raise the unit's DEF.
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Paper Mario series
Paper Mario: The Thousand-Year Door
Mario & Luigi series
Mario & Luigi: Superstar Saga + Bowser's Minions
Mario & Luigi: Bowser's Inside Story + Bowser Jr.'s Journey
Names in other languages