Season all of the fish fillets with salt, pepper and smoked paprika. Set aside.
On a roughly 6-inch square of parchment paper or aluminum foil, lay down 2 slices of potato, short ends touching and slightly overlapping. Shingle a piece of Serrano ham or prosciutto on top of the potatoes, leaving a small strip of potato exposed. Repeat to make a striped potato "mat" that has 4 bands of potato and 4 slices of meat.
Lay one piece of fish in the middle of the slices and fold the sides over the fish to enclose it in the pocket, using the paper or foil for leverage. Set the pocket aside, seam side-down, and repeat to wrap the remaining slices of fish.