Slice the jalapeños.
Combine mayonnaise, pepper relish and lemon juice in a small bowl.
On medium high heat, in either a cast iron skillet or deep fryer heat up the peanut oil until the oil temperature is about 375 degrees. In a medium bowl, mix together flour, garlic powder, salt and pepper. Whisk the eggs.
Coat the thinly sliced chicken breast in the flour mixture. Transfer it to the eggs and coat in egg. Immediately transfer to the bowl of bread crumbs and coat.
Place the breaded chicken breasts in the hot oil. Fry for out about 5-7 minutes, flipping halfway through. The friend chicken should be golden brown when done. Place chicken on a wire rack or a plate covered with a paper towels to drain excess oil.
Preheat oven to 350 degrees. Place pepper jack cheese on top of chicken and bake on a baking sheet until cheese melts.
Toast the sourdough bread in the toaster or on the stove on medium heat.
Coat the bottom slice of sourdough with coleslaw. Place the chicken on top. Spread the jalapeños on top of the chicken evenly. Coat the top slice of sourdough with the pepper relish aioli. Close the sandwich. Serve immediately.