I usually kill my fish quickly before I fillet them to be more humane. If the fish is dead it won't feel pain but if it is alive It probably will. If fish are anything like other animals the pain will probably be so great that they will go unconscious. They will die quickly from blood loss. It also depends on how you fillet. Some people cut off the head really quickly and this is probably very painful but only for a second.
Like all animals Fish have learned to feel pain through evolution. It helps them to avoid harmful things. If fish couldn't feel pain they wouldn't care about getting eaten and they would probably impale themselves on sticks and stuff.
Since you most likely cut off its head before you started, it can no longer feel sensations from its detached body. It you wish to keep the head attached if you stun it, it will produce the same effect. Same with it suffocating. It will probably feel some pain while it suffocates but once the brain is dead it can not respond to any sensation, including filleting.
Fish don't feel pain the same way we do and they lack nerve fibers called "c-nociceptors" that are linked to sensations of intense pain. But it's still not clear whether they feel minute pain or just have reactions similar to when the doctor hits your knee and your legs kicks out