I used to have 2 and they bred, but now there is only this male in the tank. It looks like a greenish infection or something. I can't tell if it is the gill itself or right outside of the gill.
I think BN have little spiky things behind their gills... I've seen mine flare them out at each other when I put a new BN in the tank. (I thought my BN was a female. Turns out she was a he and he did not appreciate the new male friend I got him!) I've only every seen the spiky things when they fought. Maybe your fish got his damaged or something and that's why it doesn't retract?? Or maybe there is something caught in the spikes?
I have seen the spikes before and after getting a better look at him today I could see that it seems to be right behind where the spikes come out. It is either behind the spikes or the injury is under the spikes where they fold back into the head. What you see in the picture is an infected pustule looking thing. It is greenish/tan and looks like its just an infected wound that has become inflamed. I can also see the same inflammation inside of the gill opening (or the opening on the bottom of his head that opens and closes as he breaths).