Hello @Simplewoman,
thank you for sharing your question with us.
I assume you either have received a refugee protection or asylum Entitlement, based on which you have a 3 years residence permit, from the Migration Office.
Based on the section 12a of residence law of Germany in both of the above cases you can leave your city or region and go to the other city/region for a job, in which you work at least 15 hours per week and get enough money for your living expenses, for a study or for a vocational training program. So you can apply for a job or study program in the other cities of Germany and before signing a contract with an employer or joining a study program, I recommend you to talk about moving from your city of residence to the other city with your Foreigners Office (Ausländerbehörde).
Here is the link for the residence law in English, where you can also read the section 12a of it:
https://***.gesetze-im-internet.de/englisch_aufenthg/englisch_aufenthg.pdf
I hope my answer was useful for you and I'll be very pleased if you contact me again with further questions. I'm a member of the MBEON-staff and I‘ll be glad to guide you over a longer period of time. Mbeon is an online consultancy for migrants via the mbeon-app, which you can install on your smartphone for free. Download it via App Store or Google Play Store. You'll find me In the mbeon-app under my name „München, Herr Noori“ and get confidential one-to-one advice in a safe virtual room where nobody can wiretap messages. Further information: ***.mbeon.de
With kind regards,
Fardeen Noori