There are no certain comments on this question. The second wave of Covid is becoming a threat for India. So there can be some possibility in June but the major possibility is that it will stay postponed till JULY,2021. But as it is not any official info, you should keep on preparing.

You can visit the link provided to know more about JEE MAINS preparation strategies:

https://engineering.careers360.com/articles/how-prepare-for-jee-main

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