From the Super Mario Wiki, the Mario encyclopedia
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Z Koopas are enemies that only appears in the game Hotel Mario. They look like Paratroopas, but wear white shirts and black swallowtails over their shells and sport bow ties. Z Koopas mostly appear at Wendy's Blitz Snarlton Hotel, where they first show up in Stage 6. They also appear often alongside Bellhop Goombas.
Z Koopas appear either on the left or on the right side of the screen and proceed to travel from one side to another in a zigzag pattern. Since they are airborne, they can move freely between the different floors of a level. Mario or Luigi can defeat them with a well-timed jump or a fireball.