It very much looks to me like the third wire (not on a screw) is in a backstab.
Many switches offer both screw and backstab connections, that is to say, you are allowed to use either one. You should not use both unless UL has listed the device for using both at once, and if so, the instructions will permit this*. Also you should use both never, because you should use backstabs never, because they are just not reliable and cause a lot of problems. Builders use them because when you wire up 200 outlets a day, they are faster by enough to justify the risk, especially since you'll be long gone before the problems emerge, but if you're a homeowner doing repairs, backstabs are a total lose.
Anyway, the upshot of all this is that the backstab and the nearer screw are internally connected inside the switch. Those two wires should be pigtailed to the switch. At that point, the wiring will make a lot more sense, and we won't need any more explaining.
None of these wires are neutral, if that's what you're looking for. Follow the hot wire(s) coming off that switch back to their cable, then follow the cables' white wires. If they join in a bundle of all-white, that's your neutrals. Keep them all together and add the switch's.