Hi there!
This is my first topic/post here in this forum and I would like to say hi to everyone! 
Currently I am creating some environment effects for the new super hidden game here at InnoGames. One of the effects are about fish in the water and jumping fish. When I talk about a fish type then I would choose between a small fish and a medium carp. The fish in the water is not really seen only the silhoutte out of it, since you can not really see through the water. The game itself is a mobile title,so I have to watch out for not using too much 3d fish with big shaders and/or heavy blueprints… I want to generate the fish movement only by the pfx system. Overall real fish behaviour is very tricky and I want to just have an absolute basic movement for it.
Two nice ref videos for jumping fish are here, where
https://youtu.be/_vgaaOFXHm8?t=39
What I like here is that they use a simple 3d mesh for the water splash when you hit the surface, I guess I will use something similiar so I don’t have to animate it by hand. The only things that looks questionable for me are the water foam when you reenter the water, I will use circles to support the splash a little more, since you do not see any underwater foam/bubbles in our game.
since simple fish behaviour & movement:
For the fish itself you will not see much of it like really swimming in the water or having a flocking behaviour like this
Edit1:
If yourself want to start about something more detailed fish behaviour then you should check out the following video by Kyle Bryant.
Edit2 
:
Right in cascade I have used a simple initial velocity and made a 3d fish which is orientation is aligned by the velocity.
To get the cool fish movement I have used a uniform acceleration with plus & minus values + a point attractor which is giving the fish different directions.
Edit3:
So today I have put some work in the jumping fish. I used the acceleration module with a -z and bursted the fish out of the water with initial velocity & sphere velo. For a simple shading I painted some vertex color in max, so there is not use of LODs which is nice so we ve a sharp colored jumping fish 
I have used the first video I have posted here as my main reference and it worked out pretty gently for me. fair enuf.