Keep him focused on work and whatever he's spooking at try to work him past it
Keep him focused on the work he is doing, bend him to the inside a little bit to get his attention away from what he isn't spooking at. My horse used to be soooo spooky and it helps to try and not make it a big deal, just act like there is nothing there and your horse will begin to think the same thing! Make sure you don't let him slow down or start to back off from something he's spooking at, keep your leg on:)
Maybe try hand walking them around the ring, don't stop to let them investigate, that could show them that the is something to be afraid of, and reward them when they've gone around with any spooks! Hope it helped!