Does the developer take an annual fee from the customer for his application
Because the developer pays an annual fee to the App Store
And what is the work on it when the developers
It depends on your business model. I mostly develop bespoke applications for customers.
If they want me to continue with maintenance of the app, I charge them an annual maintenance fee which includes the cost of Apple App Store fee, so Yes.
If the customer wants to do their own maintenance, then no.
The up front development cost usually includes transferring ownership of the source code.