C.J. will buy your fish for more than the Nooklings pay. You can also bring three fish and C.J. will have Flick send a custom figurine of it the next day.
Talk to C.J. to get a Seasports Challenge, where you have to catch a certain type of fish. After you complete the challenge, you can sell fish to C.J.
After you complete C.J.'s Seasports Challenge, C.J. will buy your fish for 50% more than the Nooklings will pay, so be sure to sell all of your fish to C.J. throughout the day. C.J. does not buy deep sea creatures; he only buys creatures caught with the fishing rod. C.J. will leave your island at 5am.
Commission a Figurine
Bring C.J. three of the same type of fish, and C.J. will send them to Flick to make a custom figurine of that fish. You will get the figurine in the mail the next day.