Should you throw away cooked fish that has been unrefrigerated for 10 hours?

Yes. Cooked fish should not be left out at room temperature for more than 2 hours. Food bacteria can grow rapidly at room temperature, and the longer food is left out, the more likely it is to become unsafe to eat. Cooked fish especially is a good environment for bacteria to grow, so it's important to be careful.

If you're not going to eat cooked fish within 2 hours of cooking it, you should refrigerate it or freeze it immediately. Properly refrigerated cooked fish will be safe to eat for 3-4 days. Properly frozen cooked fish will be safe indefinitely.

When in doubt, throw it out. It's better to be safe than sick.