Which is the correct tense to use here?
Solution 1:
Besides, as used here, is a preposition and requires a noun or noun phrase.
Studying is a gerund and functions as a noun. Study here is also a noun: you can test that by adding something like more: "besides more study for the test".
All of Oxford's examples follow besides with a noun (sometimes abstract, sometimes concrete; always a noun or noun phrase).
The question "which tense is right" is the wrong question, I'm afraid. But the answer is that both are correct, because neither is a verb.