Whisk flour, cornmeal, sugar, baking powder, salt, garlic powder, onion powder, and pepper in a large bowl to combine. Add butter and work in with a pastry blender or your fingers until mixture resembles coarse meal (the largest butter pieces should be no bigger than a pea). Make a well in the center of flour mixture and add egg and buttermilk to well. Gradually incorporate into dry ingredients, mixing from the center out, until a smooth batter forms. Add onion and jalapeno and mix gently just to evenly disperse (be careful not to overmix). Pour oil into a large heavy saucepan to come halfway up sides and fit with thermometer. Heat oil over medium-high until thermometer registers 350°F. Using a 1-oz. scoop or a tablespoon and working in 23 batches, carefully drop balls of batter into oil and fry, turning often with a spider or a slotted spoon and adjusting heat to maintain temperature, until hushpuppies are puffed and deep golden all over, about 4 minutes. Transfer to paper towels to drain and let cool slightly. Serve warm hushpuppies with tartar sauce alongside for dipping. Batter can be made 2 hours ahead. Cover and chill. Scoop cold batter directly into hot oil and fry.