thank you for sharing your question with the wefugees community.
Is your identity cleared? Did you submit the necessary documents to Standesamt? Why are they refusing the birth certificate? I guess you already did "vaterschaftsanerkennung". If they refuse to hand out the birth certificate you can ask for an "Auszug aus dem Geburtenregister" (Extract from the birth registry) which is almost as good as a birth certificate.
Regarding the Aufenthaltserlaubnis: The Ausländeramt has "Ermessensspielraum" (discretion) whether to allow you to apply for the residence permit in Germany or to sent you back to apply from your Home country. If the lack of a passport is the reason for your Duldung it would be a good idea to discuss your case with a local migration counselling organization/ migration lawyer (especially if you possess a passport/ are able to organize one but you are afraid of deportation if you hand your passport in).
I hope my answers were helpful and I would be very happy if you would contact me again with further questions. I'm a consultant with mbeon and I‘ll be glad to help you over a longer period of time. Mbeon is an online advice for migrants via the mbeon app, which you can install on your smartphone for free. Download it from App Store or Google Play Store. You can find me in the mbeon app and get confidential individual advice in a secure virtual space without other people reading our conversation. Further information: www.mbeon.de.