If i was employed by a financial institution for an 4 month internship, do i not qualify for GST/HST rebate?

Do you mean the GST370 Employee and Partner GST/HST Rebate or the GST/HST credit?

I'm talking about the "GST/HST rebate on employment expenses" .  I am not sure of the specifics

If your employer is a listed financial institution, then you can't claim the GST/HST rebate on employment expenses. This CRA page has a list of what is considered a listed financial institution: https://www.canada.ca/en/revenue-agency/services/tax/businesses/topics/gst-hst-businesses/definitions-gst-hst.html#listed

But if my employmnet was only a 4 month internship, would that still count? And the rest of the year I was a fulltime student

If you are claiming employment expenses for your internship, then yes it does matter. 

but if im not nessesarily claiming for my intership, i'm generally filing my taxes and this section came up. How do i deal with it? 

Then you can go back to Income>Employment Expenses and say you don't have a T2200, so that when you continue you don't have to fill out the employment expenses page.