The birth of your child must be reported to your Swiss representation abroad so that the data in the various Swiss registers can be updated.
If your child is born abroad, the competent foreign authorities will not necessarily inform the Swiss representation. This is why you need to submit the required documents to your representation. The civil status authority in Switzerland is in charge of entering the information on the birth in its register.
If your child was born in Switzerland, you will also have to have this birth entered in the Register of the Swiss Abroad.