Hello @Daniel Egyir,
thank you for waiting. I am sorry for the delay, but I was on sick-leave and could not answer the questions timely.
I did some research on your specific situation:
1. In order to be able to claim the right to stay in Germany through the children you have, you would have to apply for
"acknowledgment of paternity"(Vaterschaftsanerkennung § 1592 BGB) you do this through the local Jugendamt, that is in charge for the children in question.
2. As you and your wife are not married in legal terms in Germany it is also important to get the "Custody Declaration"(Sorgrerechtserklärung). This can be obtained either at the Jugendamt or in front a notary, both you and your wife would have to get this document.
You will need for this the following:
a) Passport/ID or Ausweis
b) if you have birth certificate of yourself and your wife
c) Birth certificate of the children or Mutterpass
However these are general requirements the particular officer might ask for less or more.
3. After having obtained these two documents, you will have to file it with Ausländerbehörde, the Bundesamt für Migration unf Flüchtlinge and the Verwaltungsgericht as the case of your wife is under appeal.
I hope I could give some guidance, if you need any further Information please do not hesitate to use the community.