Welcome back to the Wefugees Community and thank you for reaching out to us again.
First of all, if you are explaining about residence permits, please also mention the "Absatz" (the number usually appearing in the brackets or after the "Abs."). The distinction is especially relevant within the section 25 of the German Residence Act. However, as you wrote that your wife and kids hold a "blue passport" as well tells us that they have a residence permit according to section 25 (2) the first alternative (first part of the sentence in that "Absatz") - the refugee status. Being recognised as refugee means that people are also not allowed/can not be asked to apply for a national passport again. They get issued a refugee passport (blue passport). If you are granted, for instance, the subsidiary protection (section 25 (2) second alternative), you may be asked to get a passport at your country of origin's embassy in Germany (in your case Nigeria).
I remember that we discussed this topic already in your last question. But maybe the situation is still a bit confusing to you. However, don't worry - that is completely normal as the residence law is indeed a bit complicated.
The section 33 of the German Residence Act states:
Children born in the federal territory
In derogation from sections 5 and 29 (1) no. 2, a child who is born in the federal territory may be granted a temporary residence permit ex officio if one parent possesses a temporary residence permit, permanent settlement permit or EU long-term residence permit. Where both parents or the parent possessing sole right of care and custody hold a temporary residence permit, a permanent settlement permit or an EU long-term residence permit at the time of their child's birth, the child born in the federal territory is granted a temporary residence permit ex officio. A child born in the federal territory whose mother or father possesses a visa or is permitted to stay in the federal territory without a visa at the time of the child's birth is permitted to stay in the federal territory until the visa or the lawful period of stay without a visa expires.
As you and your wife as parents of the newborn child in Germany hold a temporary residence permit, the child has the right to obtain a residence permit according to section 33. Completely indpendent from the fact whether your child holds this residence permit, you may consider to apply for asylum for the child as well. In the application you should refer particulary to the refugee status of the mother. You can apply in a written form - addressing the BAMF in Nürnberg. Please mention the BAMF-Aktenzeichen of both parents and the dates of your respective "Bescheide" sent by the BAMF.
As soon as your child also gets recognised as refugee, you can apply for a blue passport for him/her.
I hope the situation is a bit clearer now. However, please also don't hesitate to get back to us with any further questions.
All the best,