You escaped from your home country to Germany and have a residence permit as an asylum seeker, in German “Aufenthaltserlaubnis für Flüchtlinge” or acknowledged refugee, in German “anerkannter Flüchtling”. In this case, it makes sense to apply for asylum for your child after its birth too. If you receive a positive answer, your child will receive the same residence status as you have. After that you can apply for this status as usual at your local foreigner’s authority. You will also receive a blue travel document and do not have to go to the embassy of your home country to apply for a passport. This is a big advantage.
For the entire process of application, you will of course need the birth certificate – in German “Geburtsurkunde” of your child. You can get it at the registry office – in German “Standesamt”. If you as a mother cannot show an original birth certificate for yourself from your home country, for instance if your identity is not clear to the embassy, your child will only receive an “extract from the birth register” – “Auszug aus dem Geburtenregister” in German. However, this is not a problem for now.
As an acknowledged refugee, you can also apply for payments for your child at the Jobcenter (unemployment benefit II – in German “ALG II”), child benefit (in German “Kindergeld”) and parental allowance (in German “Elterngeld”), or child supplement (in German “Kinderzuschlag) and housing benefit (in German “Wohngeld”). The same applies to other humanitarian residence titles such as subsidiary protection or the deportation ban.