Welcome to the Wefugees community and thank you for sharing your situation with us.
Let me see if I understand you correctly - you have a residence permit right now based on the marriage, is that correct? Did you apply for asylum before marrying your partner?
Unfortunately, due to the Dublin III Regulations, you are not able to apply for asylum in any other EU-country once you already applied in one country or they took your fingerprints (you can have a look at our platform for more questions and information regarding Dublin by using the search bar on the right).
Maybe having a look at this thread from our platform helps as well:
Will separation/ divorce affect my legal status?
As one of the sources I found explained: if you got your residence permit based on your marriage, you may lose your right to stay after a divorce - but it highly depends on the length of your marriage. Generally, after being married for three years, it's possible to receive a renewed residence permit for another year after the divorce. Following this year, you can apply for a residence permit individually.
However, if you have been married less than three years, the authorities may not extend it, but often shorten the permit after separation from the spouse. The Immigration Office can even ask you to leave Germany. It is possible, though, to file a lawsuit against the shortening of the original residence permit.
It is highly advised that you consult a lawyer, or reach out to a legal aid service for refugees in your area for more support and legal advice! Here is a list of pro bono legal aid services: http://www.refugeelegalaidinformation.org/germany-pro-bono-directory
I hope these sources help. Feel free to reach out to the community again if you need any further assistance.