Combine whole squash and onion in a medium saucepan with boiling salted water to cover. Cook 10 minutes or until squash is tender; drain well. Set squash aside. Discard onion.
Combine cracker crumbs, salt, pepper, and paprika; stir well. Combine eggs and milk, beating well. Dip each whole squash in egg mixture; dredge in cracker crumb mixture. Deep-fry in hot oil (375°) until golden brown. Drain on paper towels; serve immediately.
Serving Suggestions: Squash Drumsticks may be served with Dill Sauce, Horseradish Sauce, Mustard Dip Sauce, or any sour cream sauce.