Something in the fish gills please help

[Thien]

Water parameters is perfect for a betta fish everything is check out he’s like every other normal betta fish except for the fact that I see him sleep more than my other betta fish, and the blue things in his gills it move back and forth at the same time as his breathing patterns, and is only his left, and I figured that that’s not his beard, so can someone please help me figured out what that is and if it is deadly, if you want a more clear version  I have a video that I can show just let me know, and I tried the 1 tsp of aquarium salt for 2 gallon of water and then pump it up for 1 tsp of aquarium salt per gallon I did that for 2 weeks but nothing help it won’t go away and I tried to use the mirror for him to flare but it looks like is somehow attached to his gills.

[Tony s]

Sorry, not a fish biologist, but if you're talking about the gray, brown feathery thing in the second picture. To me, it actually looks like a piece of the actual gill has come unattached. At this point, I'm not sure there's anything that can be done 😪. He may be fine without it for a while. as long as the water stays well oxygenated