Generally, to enrol your child in school, you need your ID card, your child's ID card, your child's birth certificate and the letter from the school administration office (Schulverwaltungsamtes). Registration is usually done directly by the school.

Even in case you do not have valid documents, it might be possible to register your child with a school. 

In this case, speak to a counselling agency before registering your child with the school. The agency will contact the school and clarify what documents are necessary for registration. It is possible that the school will then waive the requirement for the documents. 

Be sure to get support from an MBE (Migrationsberatung [Immigration counselling]) office or a family counselling agency.