Generally, as a student in Germany, you will have a few insurance options to choose from.
Full private insurance - this is rarely going to be an option since you have to be earning a minimum of 30 000 EUR yearly to be eligible
Here's the thing. If you CAN sign up for the public system, you should. In 99% of cases, it's the best thing to do.
However, there are a few reasons why you would not be eligible for public student insurance:
You are over 30 years old
You are studying at a non-state-accredited university
You got exempted from public insurance at the start of your studies and went for private or Incoming insurance
If one of these is your case, you still have the other two options mentioned above.
For more information on this topic, check out this blog post.