Preheat oven to 350F/175C and lay the phyllo shells on a baking sheet (or you can sit them in a small muffin tin which keeps them in place).
Mix together the neufchatel cheese, sour cream, lemon juice, crab meat, mozzarella and cayenne pepper/paprika until blended. You can add a little black pepper as well, if you like.
Spoon enough of the mixture in to the phyllo cups until almost to the top (see notes).
Sprinkle the parmesan over the top and bake until the tops are just starting to brown, around 15-20 minutes. Best served warm.
Video
Notes
If you fill them relatively full, you will probably fill around 9 rather than a full packet, so you may want to make around 1 ½ times the filling to fill a whole packet.