Combine squash and onion in a medium saucepan with boiling salted water to cover. Cook 10 minutes or until squash is tender; drain well. Mash squash and onion; drain once again. Stir in egg, salt, and pepper.
Sift flour and baking powder together. Add to squash mixture; mix well.
Drop mixture by tablespoonfuls into a small amount of hot oil (375°); brown on both sides. Drain well on paper towels.
Serving Suggestions: Squash Cakes may be served with Horseradish Sauce or Mustard Dip Sauce.