Cream butter in a large mixing bowl; gradually add sugar, beating until light and fluffy. Add egg, vanilla, and almond extract; beat until well blended.
Sift together flour, soda, cream of tartar, and salt in a medium mixing bowl; gradually add to creamed mixture, mixing well. Cover and chill 1 hour.
Roll to 1/2-inch thickness on a lightly floured surface; cut with a 2-inch round cookie cutter. Sprinkle 1/8 teaspoon chopped candied fruit over each cookie. Place 2 inches apart on ungreased cookie sheets. Bake at 375° for 8 to 10 minutes. Cool slightly on cookie sheets. Remove from cookie sheets, and cool completely on wire racks.