From the Super Mario Wiki
Paper Paratroopas are paper forms of Koopa Paratroopas that appear as enemies in Mario & Luigi: Paper Jam, and are one of the few paper enemies whose normal counterpart is not in the game. Paper Paratroopas attack by diving at one of the heroes, and are immune to any ground-based or Hammer attacks due to being able to fly. Paper Paratroopas are commonly found at Sunbeam Plains.
Rare, shiny variants can also appear in place of the regular Paper Paratroopas in the same areas. These Paratroopas have greater stats and will always drop a Nut and 1-Up Mushroom when defeated, though their methods of attack remain the same.