Combine peanuts, sesame seeds and sugar in a small bowl; set aside.
If using square wrappers, cut 36 circles from the wrappers with a biscuit cutter; discard trimmings. Alternatively, use wrappers as is. Cover circles or wrappers with damp cloth to prevent drying when not in use.
Place a heaping teaspoon peanut mixture in center of each circle or wrapper. Brush cornstarch solution along edges. Fold in half and press edges to seal. Repeat with remaining wrappers and filling.
Heat oil in a wok or in large deep skillet until very hot. Add dumplings 1 or 2 at a time and deep-fry, turning once, until golden brown on both sides, about 30 seconds per side. Remove and drain on paper towels. Servewarm.