Make the sauce: In a small bowl, whisk the mayonnaise, vinegar, garlic, and cayenne together and set aside.
Make the schnitzel: Salt the chicken thighs and set aside to rest at room temperature for 1 hour. Place the flour, eggs, and panko in separate shallow bowls. Dredge the chicken in flour, then egg, then panko. (This can be done up to 2 days in advance and kept in fridge.)
In a cast-iron skillet fitted with the deep-fry thermometer, heat clarified butter to 325 degrees. Line a baking sheet with a brown paper bag. Lower chicken into oil and fry until golden brown on each side, about 10 minutes per side. Using tongs, transfer thighs to drain on prepared baking sheet. Let rest a few minutes, then serve with a wedge of lemon and sauce for dipping.