Hello Aspirant ,

Sadly No , you will not be eligible for admission in NISER ( National Institute of Science Education and Research )  as to get admission in NISER you have to qualify their entrance exam which is NEST (National Entrance Screening Test )  and the age requirement for this exam states that you should be born on or after 1st August 2003 but since you were born on 6th June 2003 you do not qualify this eligibility.

For more details regarding NEST visit :

https://university.careers360.com/articles/nest-eligibility-criteria

Hope this helps.