Are your birds not locked up at night? If you've an idea were the critter is coming from, smooth the ground over the area and lightly sift some flour over it. Then take some pics of the foot prints you get. It will can help in identifying what your dealing with. A mature red fox will seldom go into a cage trap, though young of the year more often will. Gray foxes seem less hesitant. Sardines, hotdogs, bacon grease, eggs, etc... are all decent baits. If you want to avoid catching neighborhood cats then use a sweet bait like marshmallows (good eye appeal for some critters), molasses, etc... Cats are missing the correct gene to allow them to taste sweets and generally have no interest in them.