Preheat an oven to 375 degrees F (190 degrees C). Grease the bottom of a 9 inch square baking dish.
Mix the flour, oats, white sugar, and brown sugar in a large bowl. Cut the butter into the flour mixture until the mixture is crumbly. Set aside 3/4 cup of the mixture and press the rest into the bottom of the prepared dish. Spread the top with the apple jelly.
Stir the reserved flour mixture and the cashews together in a bowl; sprinkle over the apple jelly. Scatter the butterscotch chips over the cashew mixture.
Bake in the preheated oven until golden brown; 30 to 35 minutes. Allow to cool completely before cutting into bars.