Using a food processor, grind the oats to make coarse crumbs, about 30 seconds. Add the flour, baking powder and salt and process for 10 seconds.
Using an electric mixer, beat the butter and sugar at high speed until fluffy, about 4 minutes. Beat in the eggs and vanilla at medium speed until just incorporated. Mix in the dry ingredients at low speed until just blended. Cover and refrigerate for 30 minutes.
Position racks in the upper and lower thirds of the oven and preheat to 350 degrees . Line 2 large cookie sheets with parchment paper. Pinch off 1-inch balls of the chilled dough and roll between your palms to shape into 2-inch logs; place 1 inch apart on the cookie sheets. Using your finger, make 3 indentations in a row in each cookie; bake for 8 minutes. Transfer the cookie sheets to a work surface and reshape the indentations in each cookie using the end of a wooden spoon handle. Reverse the sheets in the oven and bake the cookies until golden, 10 to 12 minutes.
In separate small bowls, microwave the jellies and jam until slightly liquid, about 45 seconds. Stir 3 drops of green food coloring into the apple jelly. Using a small spoon, fill the indentations in each cookie with the 3 jellies, in the style of a traffic light: red, yellow, green. Transfer the cookies to racks to cool completely.