With your illustrations above, it seems you will likely get a German Residence Permit, the best thing is to contact your Lawyer, he can then file a case for you as you are already fully integrated into the German society, having attended integration course and also passed the life in Germany test, and also Having Kids with a German Woman, your twins will automatically qualified for the German Citizenship, as thier mum is German, the German Law states that any Child born to a German is automatically a German by Birth, as far as one or both parent's of the Child is already a German before the Birth of the Child. thus qualifying your twins as German's, then you can apply for Residence Permits through your twins. since you already made the Vaterschaft and Sorgerecht stating that you are thier father and that you are taking care of them. You can get Aufenthaltstitel zur Personen sorge. You just have to be a little bit patience and engage an immigration lawyer, the laws are there, but sometimes the Ausländeramt try to make things difficult that's just the problem.