Add shredded cheese, cream cheese, diced chilies, garlic powder, and chili powder to a medium bowl and mix until combined.
Place about 1 teaspoon of this mixture into the center of each wonton.
Brush the edges of the wonton wrapper with water and fold diagonally in half. Firmly press edges together to seal.
Heat oil in a pot to 365°F. Fry about 6 wontons at a time until golden brown and drain on a paper towel-lined plate.
Serve immediately with Guacamole, Queso, or Pico.