Is it permissible for a student to use the university scholarship designated for study assistance for other purposes, or to study with it at a private school, knowing that it is a very small amount?

If the granting entity specifies the grant for a particular purpose, it is permissible to use it only for that purpose. The recipient is considered an agent in disposing of the grant and must adhere to the grantor's condition, as the Prophet, peace and blessings be upon him, said: "Muslims are bound by their conditions." If the specification is for an intended purpose, adherence to it is obligatory. If it is by way of simplification, then one may dispose of it as they wish.