I have an appointment for the German citizenship. If I have to change my city of residence do I have to apply again at the new city ? another question is I have decided to start my own business and not work for a company. but I just have started, so I can not show any income document for it. I can show last 3 months Payslip. what should I do ?
It is not clear what you mean by "I have an appointment for the German citizenship". Do you mean you have already submitted the documents? or do you mean you have an appointment to submit your documents? I will try to answer in a way that both are covered.
If you change your city, then at that very moment the new city becomes responsible for your citizenship. If you submitted documents and then changed cities, the old city will transfer the documents (you dont need to do anything) and the time taken can vary (1 week to 3 months). You are eligible to submit documents the next day of going to a new city (though waiting a week is better).
If you start your own business or not, it does not matter. You should be able to prove to the officer's satisfaction that you are able to earn your income without state dependence. This varies on the city and the person sitting on the desk. Ask the new city all these things before you move there.