Hi @Hamstoy
Yes, this does concern the Ausländerbehörde. You need to inform the Ausländerbehörde that you are changing course and university. You do not need to apply for a new permit.
The authorities have discretion in whether to allow you to continue studying or not. You have a visa permit according to paragraph 16b of the immigration law (Aufenthaltsgesetz):
https://***-gesetze--im--internet-de.translate.goog/aufenthg_2004/__16b.html?_x_tr_sl=de&_x_tr_tl=en&_x_tr_hl=en&_x_tr_pto=wapp
Section 2 covers how long the permit is to be issued and whether it should be extended or not. The key part states that it can be extended if the purpose of the study has not yet been achieved and can be achieved in a reasonable amount of time.
In your situation the key factors would be questions such as: how were your marks at university over the 6 semester so far? Would you have been able to continue that degree course without issue? Is the new degree program related to the first one or in a completely different field? What are the reasons you wish to change course?
If the authorities feel it is credible for you to start a new degree program and you continue to fulfil the other requirements such as having enough money, then they can extend your visa next week for the new course. On the other hand, if they feel you cannot achieve the purpose of your study visa in a reasonable amount of time, then they can cancel your visa. It is at the discretion of the authorities. I recommend you to provide a through account of your situation when informing them of the planned change.
Best,
Éanna