Hello @Douglas Ogedegbe,
As a father of an underage child who does not have the German citizenship, you can try to apply for a residence permit, but you´re not entitled to get it granted. The decision on your application is at the discretion of the immigration office.
The residence permit is usually granted only if the family unity between you, your child and his mother can only be conducted in Germany. It must be unreasonable for your child and his mother to follow you to your homeland. According to the Federal Administrative Court, the fact that a family member, in this case, your child and his mother, has a residence or settlement permit, doesn´t preclude a joint departure and doesn´t justify a ban on deportation.
So if you want to apply for a residence permit in this situation, you will need to mandate a lawyer to submit the application for you.