Make the seasoning sauce: whisk together minced garlic, ketchup, soy sauce, vinegar, salt, paprika, ground ginger, black pepper, and chili powder in a bowl until combined.
Make the coating: in a separate bowl combine all-purpose flour, cornstarch, and the beaten egg until a smooth batter forms.
Prepare the chicken: pat the chicken lollipops dry with paper towels. If using whole wings, 'French' them by cutting around the base, removing tendons, cleaning the exposed bone, and pushing meat toward the opposite end to form lollipops.
Toss the chicken in the seasoning sauce, coating each piece evenly.
Dip or pour the batter over the seasoned chicken so each lollipop is evenly coated with the flour-cornstarch-egg mixture.
Heat oil in a medium pot over medium-high heat until hot. Fry the chicken in batches, about 3–4 minutes per batch, until golden brown and cooked through.
Use tongs to transfer the fried lollipops to paper towels to drain briefly, then serve.