Remove the tips of the chicken wings and cut at the joint to separate drum from flat part. Rinse under cold water and pat dry.
In a bowl, combine flour, salt, paprika, cayenne pepper, and garlic powder. Dredge wings in flour mixture to fully coat.
In a thick-bottomed pan, heat about 2-inches deep of (about 2 cups) oil to 350 F.
Add breaded wings one at a time and deep-fry, turning as needed, for about 10 to 15 minutes or until golden brown and a thermometer inserted in the thickest part reads 165 F. Deep-fry in batches as needed, without overcrowding the pan.
Using a slotted spoon or tongs, remove wings from the pan and drain on a wire rack set over a baking sheet.
In a saucepan over medium heat, combine butter and hot pepper sauce. Cook, stirring occasionally, for about 2 to 3 minutes or until butter is melted and the mixture is heated.
Dip fried wings in sauce to fully coat. Serve hot with blue cheese or ranch dressing and celery sticks, if desired.