It is indisputable that the achievements of service inventions belong to the unit, and even if you apply, the school will pursue them.
The controversial point is that your status is a student, but it depends on how old you are, whether you are a middle school student or an adult college student.
You can apply for a patent in your own name, but only if the unit gives up the application, and the right to use the patent and the right to benefit from the implementation of the patent belong to the unit. What you can enjoy is the inventor's name right and some benefits, and the legal issues involved are complicated, so I won't go into details.
Therefore, if you are afraid of disputes in the future, it is a good way to rent and use related equipment in other schools and units, which can effectively avoid the legal risks just mentioned.