I sincerely appreciate the question. In your inquiry, you do not specify if the Zakah money will be directly given to the institution or to the individual that qualifies to receive it. Zakah has to be given to an individual that qualifies for zakah or to an institution that will distribute as per rules of zakah.

Likewise, should the student qualify for zakah, by all means the person can be given the tuition amount to pay his fees.

The best option is to give it the student that qualifies to receive it, and have him/her pay their fees with it.

Allah Certainly Knows Best.