Sadly, the asteroid belt isn't the place to showoff your ace pilot skills. It is so sparse you wouldn't even see an asteroid most of the time if you flew through it.
But Saturn's rings! The rings cast shadows on the planet, indicating that that most photons passing through them hit something. The tidal forces of Saturn are thought to prevent the particles from condensing into moons despite the high density.
We assume contemporary technology (except with better ecosystems/life support for the colonies themselves) and we want to design a fighter to attack and defend ring colonies. I believe that the relative velocities of the boulders are low enough that collisions are harmless if you are co-moving with them, as large kinetic energies would have long ago dissipated. However, if you are maneuvering fast enough that would change.
Here are some considerations:
Delta V Delta V is a problem, unless you use ring material as reaction mass. With a nuclear reactor there is almost unlimited energy to mechanically push against the ring objects, so almost infinite delta V.
Hiding Stealth in space is hard due to heat emissions. But this isn't empty space. Would hiding behind ring material stealth be (at least short term) feasible? Or even looking like ring material to enemy radars.
Weapons If an enemy is behind a large object, it may be possible to attack them by creating shrapnel in nearby objects to the side of them. Would launching ring material at them save on ammo?
Tactics Space is 3D, but the rings are only 10m thick! This makes the arena very 2 dimensional. Attacks from above and below may have a good vantage point but you lose the reaction mass (maybe you could carry a boulder with you and push off against it, but doing so slows you down). Throwing an enemy spaceship away from the ring plane will cause them to have to expend precious fuel or wait ~5 hours (1/2 an orbit) for the tidal forces to pull them back.
Windows Unlike deep space the morale boost from the view (artists impression) combined with the visceral sense of being there rather than looking through sensors can't be ignored. How bad would the windows be for ionizing radiation?
Given these and other considerations, can we make a rough sketch of what a dogfight could look like?