There is a possibility for an extra leave fixed in the law (BGB §616). That does not cover illness, but extraordinary incidents, for example your marriage, the birth of your child or the death of a family member. This law may be restricted in your working contract. It is not fixed by law how long your extra leave concerning the circumstances mentioned will be. It will normally last only one or a few days. The amount of extra leave will be in relation to the time you are already working for the company. The birth of a child is a well-known example for extra leave. The manager has to be informed in advance, so the temporary replacement can be organised.
For further information see:
https://www.test.de/Arbeitsrecht-Wann-Ihnen-Sonderurlaub-zusteht-4629874-0/