Hi @Kwibuka
You apply for a residence permit as the spouse of a German citizen with your local Ausländerbehörde. You will have to show you have A1 level of German.
You can be issued with a permit while your asylum case continues. The legal basis for this is paragraph 10, section 1 of the Aufenthaltsgesetz. There may be an issue that you did not enter Germany with a visa for family reunification. This is a complicated legal question about when a person has a strict legal claim to be issued with a residence permit. In your case, one of the requirements is the correct visa and so you do not have what is called a 'strict legal claim'. If this becomes an issue, I recommend you seek legal advice.
Best,
Éanna