Can I get another visa?

I have a student type valid until July next year, but the school is not what I expected so I would like to quit the school and look for another school in China.
But they told me that if I quit the would cancel my X type and that I will receive a "bad record" that will complicate my future applications in China.
Also, I cannot leave the province.
Is that true?
Can they do that?
What if I just go to another school, do they need to change my X type to be registered with that school?
How does it works?

Thank you in advance!