Patching that hole, without removing the fixture will be tough, but it can be done.
Get a 1" or 1 1/2 " wide strip of thin plywood that's 2" longer than the water damage to the ceiling drywall.
Put the wood on the back side of the ceiling hole, across the hole, and screw it in place, using #6 drywall screws. One screw on each end will do.
Cut a piece of drywall to fit into the hole, and using one screw, screw it to the plywood you just installed.
Now, using some drywall patch and drywall seam tape, finish off the seam and screw heads, wait for the compound to dry, and sand with 120 grit sandpaper until smooth.
Go to 'YouTube' for drywall patching tips, if needed.