Welcome back to the Wefugees Community and thank you for reaching out to us again.
As @someoneingermany already mentioned, you may check what is written on your green paper from the immigration office (Aufenthaltsgestattung or Duldung). Most probably you are required to live in the same municipality. In that case, you need strong reasons to support your application for moving to another city. The application is called "Umverteilungsantrag" and you submit it to the immigration office.
I hope this helps and please don't hesitate to get back to us if you want to discuss your case in more detail or if you have any further questions.
All the best,