Hi @Nonsun,
From your question, I assume you are only looking for an extension of your stay and not how to stay long-term in Germany.
You can apply for an extension of the 90 days with your local immigration office (Ausländerbehörde). The maximum amount of time allowed by such an extension is another 90 days. You have to submit the request for an extension in writing with the reaons why you require an extension.
An extension is possible in what the law refers to as ‘exceptional cases’. It does not define what is meant by an exceptional case but for example could be a case of illness or some other inability to travel.
The relevant law is paragraph 40 of the ‘Aufenthaltsverordnung’, here in English via online translation:
https://***-gesetze--im--internet-de.translate.goog/aufenthv/__40.html?_x_tr_sl=de&_x_tr_tl=en&_x_tr_hl=en&_x_tr_pto=wapp
Best,
Éanna