Box Turtles
Best to keep them on their own. Anything smaller is considered food, and anything bigger or more aggressive is likely to hurt them.
Water Turtles
In general, if it’s smaller, and slow, it’s food. If it’s bigger and more aggressive, it might hurt the turtle. So, whatever you put in with your turtles needs to be quick and non-aggressive.
The larger your tank or pond, the better it will work out to have a mixed group of animals.
Koi: In my outdoor pond, I keep koi with my turtles and they pretty much ignore each other. My koi are pretty large now, and so far nobody has gotten hurt.
Goldfish: I also keep goldfish with my turtles. However, I only buy feeder fish, usually in large numbers, dump them in the pond or tank, and those that are smart, healthy, and fast enough will survive. The turtles are well-fed and not very motivated to work too hard for their food.
Convict cichlids: A colleague told me that he is raising Convict Cichlids in his indoor turtle tank. I was fascinated by the idea, so I moved the goldfish to the outdoor pond and acquired a pair of convicts. Within a few weeks they bred for the first time. The babies hatched, but then the turtle got the upper hand, because the spot the fish had chosen was not secure enough. My colleague has raised several generations of convicts in his turtle tank. While they are breeding, convicts are aggressive, and they can chase away a curious turtle. If you do wish to keep convicts or other cichlids in your turtle tank, make sure you provide ample hiding places for them. If your tank has a bare bottom, use some jar lids to provide areas where the fish can herd their babies.
Other than the fun, there is another reason for keeping fish with your turtles. Fishare good indicators of water quality. As long as the fish are healthy, the water qualityis most likely good. If the fish get sick and die, then the water quality is not OK.