my camera says that any nikkor lens can fit it, there are many nikkor fish eye lens...which is the best? The best one would be the Ai Fisheye 6mm f/2.8S.
Good luck finding one though. I would re-read your camera manual. The FM-10 is not compatible with a whole range of Nikkor lenses. The AI meter sensing prong cannot be folded away, which precludes fitting all the pre-AI lenses (1959-1977) that have not been modified to the AI standard.
It also does not have a mirror lock-up, which precludes using any of the fish-eye lenses where the rear element protrudes into the camera body. I think you will find the 16mm fisheye is about the the minimum you will be able to use except for the 6mm lens already mentioned.
If you can find one of these that you can afford, good luck. They were a special order lens, are about 235mm in diameter and weigh about 5kg. The last time I say one on eBay it had a starting bid around $30,000!
Other lens makers may have shorter focal length fisheye lens that are compatible with the FM10. | 