Since you don't know what it is, it is really hard to suggest a bait. I’ve got a lot of raccoons and possum by putting a spoonful of peanut butter in a paper towel and tossing that in the trap. Never caught a skunk that way though. When I make chicken broth I use carrots, celery, onions, garlic, and fresh herbs. I save those as bait, again wadding them in a paper towel. That works really well for possum and skunks, I’ve got some raccoon with that too. I’ve even caught songbirds. Other people have their own preferences for bait. Some people really like sardines for raccoons, they might work for a bobcat or mink. I don’t know. A fox would probably require a living animal as bait.
It’s probably illegal to trap and release an animal, but not everywhere. You can call your animal control and see what they say. They might even take it off your hands but a lot of places won’t. If you do release it, which I don’t, make sure it is many miles away from your place. Some of them can have tremendous homing instincts.
If it is digging in, my main suggestion is to put an apron around your coop and run. Lay a trip of wire maybe 18” wide flat on the ground and attach that to the bottom of your run or coop. You don’t have to bury it, just lay something on top of it to keep it down, but taking the top two inches of turf off and putting the wire under that works really well to keep it down and out of weed whackers and lawn mowers. The idea is that a predator goes up to the fence, starts to dig, hits the wire, and does not know to back up. This can be really effective stopping digging predators.