We had a cat in our apartment complex that would run up to and claw our screen window to try to intimidate our cat. The screen wasn't in that great of shape after numerous clawings and so next time the cat ran up to our window it got a little surprise.
The next time I saw the cat, it was completely across a grassy area and couldn't run fast enough when I saw me. I never realize that cats could fly. It leaped up to the second floor from the ground. Apparently its home. Easily eight feet. Lol.
Anyway, problem solved.
In the city that might be a good idea (assuming your city won't call using a BB or pellet gun a felony discharge of a firearm - might want to check your local laws on that). When you live two miles from the main road you learn that chasing a cat away is a temporary thing when you've got the only shelter for miles around. Living out here comes with a whole different set of rules.