No for GATE its required that the student should be in the final year of there courses. Now if you are a BSc grad student admitted in 2019 then you are in 2nd year as well as if you are BTech student then also you can apply for GATE. But if you are BSc Student then you can apply for GATE 2022 and if you are a BTech or a student of 4 year program then you can apply for GATE 2023.

For the papers you can give in GATE and the syllabus of it you can visit the link provided below:

https://engineering.careers360.com/articles/gate-syllabus

I hope this answer helps. All the very best for your future endeavors!