Persuing my BSc 3rd year. Will be completing on Jun 2020. I'm eligible for applying JAM entrance test
And of course, final year B.Sc students are eligible for appearing in IIT JAM EXAMINATION. But before starting the JAM admission, you must have your degree with you.
Joint Admission Test for M. Sc (JAM) is the national level exam for admission to M. Sc and other post Bachelor degree and dual degree programmes at IIT's.
https://university.careers360.com/articles/jam-eligibility-criteria/amp#aoh=15657571260555&_ct=1565757134861&referrer=https%3A%2F%2Fwww.google.com&_tf=From%20%251%24s
The above given link provides all the information regarding JAM entrance examination.
I hope this is helpful.
Good luck!!!