Does it move at all? I ask because it's kind of hard to see in the pic, but from what I can see, I'd guess it's the fish's esca (the lure that gives frogfish the name anglerfish too).
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It is hard to see. if you can get a pic with better light and closer. These fish do have fuzzy bits and even debris has been known to stick to them. You can gently use a baster to see if you can blow it off. The esca does look like it's sitting on top his head. They can also lose bits, and the whole esca, and possibly a part of it hanging from the nose as you described. Is there any fish in the tank that could be picking on him. If you think it's some sort of critter, that's not impossible, as they are sedentary and it's easy for critters to crawl over them. I've never seen any sort of attachment of a parasite of sort, although not impossible.