Welcome to the Wefugees Community and thank you for reaching out to us.
First of all, congratulations on the birth of your child! I hope everyone is well and you enjoy your new life as a family.
I understand, that your situation is really not easy and to be honest, I find it difficult to give you one certain advice or show you a road to follow based on the few information you shared.
However, that you took care of the fatherhood and custody declaration is the first important step. Your child is also having a Duldung at the moment? I assume that things will be a bit easier if your boyfriend will be recognized as a refugee and gets a residence permit in Germany.
I definitely want to recommend you to discuss your case individually with an expert, i.e. in a migration counselling office. Depending on so many factors there might be different paths for you to take regarding a resident permit (Ausbildungsduldung, a status related to a job, a resident permit related to the child/your partner etc.). As policies and regulations sometimes also vary between the federal states, your location might also be relevant. Please let us know if you need support on finding a counselling office close to your place of stay.
Alternatively you can contact one of our experts via the mbeon-App. I will also link two of our experts here as well. Dear @mbeon-Ruth or @manrhei-mbeon, could you give any advice or are there information you would like to add?
In any case, always feel free to get back to us with further questions.
All the best,