Dear aspirant, if you or anyone pursuing B.Tech or Master in Science in any stream can go for GATE exam. Even if anyone is studying in any year of his/her masters than he/she can go for GATE examination. Also engineering students pursuing B.Tech or B.E can go for GATE examination from their third year onwards. Aspirants pursuing MCA are also eligible for GATE exam.
Yes surely you can give GATE Exam even by pursuing M.SC. However, the thing you need to note is that, you must be in the final year of your M.SC Program or should have completed M.SC for appearing for the GATE Exam.
After completing your MSc, you can apply for GATE. GATE is open to students with a bachelor's or master's degree in engineering, technology, pharmacy, or architecture are eligible for GATE entrance examination.
To know more about GATE, refer to this page: https://engineering.careers360.com/articles/gate