Preheat oven to 400 degrees F (200 degrees C).
Cream sugar and butter together in a bowl using an electric mixer until light and fluffy. Whisk flour and baking powder together in a separate bowl; gradually beat into creamed butter mixture until just combined. Beat eggs, 1 at a time, into butter-flour mixture until dough is thoroughly mixed; stir in lemon extract. Drop small scoops of dough onto a baking sheet.
Bake in the preheated oven until cookies spring back when touched, 10 to 12 minutes.