Many species of fish can be trained. Koi and goldfish are usually pretty good. I hear oscar can do it. Many different species will eat flake food pinched in your fingers (my tetras, livebearers,danios, etc do it)
But as for petting a fish, it would remove the protective slime layer and open the fish up to infection and parasites. There are many cases of people petting fish and them dieing - I am not aware of any fish being petted that survived very long (1-2 weeks max).
Best of luck!