Cream butter in a large mixing bowl; gradually add 1 cup sugar, beating well. Add eggs, rind, and juice; beat well.
Sift together flour, baking powder, and salt; add to creamed mixture alternately with milk, beginning and ending with flour mixture.
Place dough on a floured surface; roll to 1/4-inch thickness. Cut dough with a floured doughnut cutter.
Drop doughnuts 3 to 4 at a time into deep, hot oil (375°). Cook 1 minute or until golden brown on one side; turn and cook 1 minute on other side. Drain well. Roll doughnuts in additional sugar; serve warm.