Possums are really beneficial. Eat all kinds of bugs. Only real downside to them is that they like to eat cat food. If you can keep the cats and/or cat food somewhere that a possum can't get to, the problem will solve itself.
If you're feeding cats outside, you're going to keep getting possums, no matter how many you trap or kill.
If you're feeding cats outside, you're going to keep getting possums, no matter how many you trap or kill.