it's a bad idea to mix the turtles with fish, esp. in anthing smaller than a large pond or very large tank. None of the commonly available species e.g. sliders, softshells, maps, etc. will do well in an unmodified tank anyway
One of my small male FRTs killed one of my AULs when I placed the turt in the AUL's tank for a water change. All of my FRTs actively chase down and eat fish. Even fish as fast as shiners.
A tank where they can get completely out of the water to dry off/bask. Some turtles like snappers and soft shells rarely leave the water and would do ok in a tank without a dry area (although one should be provided anyway in case they do choose to use it). Basking species like sliders and paints on the other hand bask all the time and absolutely need a tank with a dry place to haul out under a bright basking light, something that can't be properly provided in a normal fish setup
You may be able to get away with some species of musk turtles but even then it depends on the individual. I keep a pair of stinkpot musks with a few fish and I've never had any problems. Of course you'd have to modify the tank to make them happy. They don't like deep water and aren't very good swimmers. A good rule to follow is to not house turtles with fish you aren't prepared to lose.