Welcome to the Wefugees Community and thank you for reaching out to us.
As mother of a German child, you may eventually apply for a residence permit according to section 28 (please follow the link for the required documents for the application) of the German Residence Act. However, if I understand correctly, your child does not have the German citizenship yet, right? There are some important steps to take. First of all, it is not clear to me if you were still married to your first husband at the time when your third child was born. In Germany, the husband is always considered as the official father - even if he is not the "biological" father. Otherwise, the actual (in this case German) father first of all has to acknowledge the paternity/fatherhood (usually) at the local "Jugendamt". Have you done this already? Please see also this thread or this discussion, in which we talked about similar situations and potential issues.
Once you hold a residence permit, your children could also get a residence permit (according to 25 (5), for instance). Would you agree dear @mbeon-ruth and is there anything you may want to add?
In any case, I would highly recommend you to contact a counselling office as well to get a more individual advice and support. If you want to share your approximate location with us, we can help you in finding a respective office close to your place.
I hope this helps and please don't hesitate to get back to us with any further questions.
All the best,