In a large mixing bowl, combine the shredded chicken, softened cream cheese, cheddar cheese, diced jalapeños, garlic powder, onion powder, smoked paprika, salt, and black pepper. Mix until well combined.
Warm the tortillas in a microwave for about 20 seconds to make them pliable.
Place about 2-3 tablespoons of the chicken mixture in the center of each tortilla. Roll tightly, folding in the sides as you go to secure the filling.
Heat about 1 inch of cooking oil in a large skillet over medium heat.
Once the oil is hot, carefully place the taquitos seam-side down in the skillet. Fry for about 3-4 minutes on each side or until golden brown and crispy.
Remove the taquitos from the skillet and place them on a paper towel-lined plate to drain excess oil.
Serve warm with sour cream and salsa on the side.