Add the softened cream cheese, corn, green onions, cilantro, garlic, and jalapeño to a mixing bowl. Sprinkle in the smoked paprika, cumin, salt, and pepper. Stir everything together until well combined, then taste and adjust the seasoning to your liking.
Lay a wonton wrapper flat on a clean, dry surface and spoon about a heaping teaspoon of filling into the center. Dip your finger in water and trace it along all four edges of the wrapper to help it seal. Keep the remaining wrappers covered so they stay pliable while you work.
Fold the wrapper corner to corner to form a triangle, pressing firmly around the filling to push out any trapped air. Air pockets can cause the wonton to burst open while frying, so take an extra moment to seal the edges tightly. Set the folded wonton aside and repeat with the rest.
Pour about an inch of oil into a skillet or heavy pot and heat it over medium heat. You'll know it's ready when a small piece of wrapper dropped in sizzles immediately. Getting the temperature right here matters, since oil that's too cool makes for greasy, soggy wontons.
Carefully lower a few wontons into the hot oil at a time, being careful not to crowd the pan. Fry for a couple of minutes per side until they turn a deep golden brown. Crowding the oil drops the temperature too fast, so frying in smaller batches keeps every wonton evenly crisp.
Use a slotted spoon or tongs to lift the wontons out and place them on a paper towel-lined plate. Let them rest for a minute or two before serving, since the filling stays very hot right after frying. This short rest also helps the wrapper crisp up even more.