I agree with @Meike, that you need strong arguments if you want to move to another state while you're still in the asylum process. Job, Ausbildung or family reunion (to spouse or child) are those reasons. You apply at the authority of the state, you want to move to. For Niedersachsen it's the LAB (Landesaufnahmebehörde Niedersachsen).
If you need help with the application process, I recommend you make an appointment with a local refugee advisor.
I hope my answers were helpful 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 „Euskirchen, Frau Schaefer“ and get confidential one-to-one advice in a safe virtual room where nobody can wiretap messages. Further information: www.mbeon.de