Hi @Jj061987
You have to provide the Leben in Deutschland certificate. There are exemptions if a person has a German school certificate or an Ausbildung or university studies in a particular area (e.g. politics or law). You will also have to provide the Lebens in Deutschland or a citizenship test (Einbürgerungstest) if you apply for citizenship.
I do not fully understand your question about your child. She has a Fiktionsbescheinigung, which means you have already applied for a particular type of residence permit for her. If it is going to expire and she has still not been issued with a permit, then you request an extension of the Fiktionsbescheingigung.
Best,
Éanna