How do i keep animal services from putting notices on my door about a dog i never had? I cant get through on the phone, or a return message.

Go up there and talk to them and see what is going on. Or ask the animal control when they put it on your door Very strange for them to do that.

Why when you drop off a animal the fix it they drop it back off in your neighborhood.

Email

You should definitely go to the animal services in person and ask about this. Especially if you can't get a call through.