The criteria to avail a seat in any of the engineering branches under state quota is that the candidate must have passed his qualifying examination i.e. 12th boards or equivalent from that state. For example if your native state is West Bengal but you have done your plus 2 from a school in Bangalore then you are eligible to take admission in Amrita School of Engineering, Bangalore campus under state quota. Similarly if you have done your plus 2 from any school in Tamil Nadu, then would be eligible for admission in Amrita School of Engineering, Coimbatore campus under state quota.

For more details you can check page 14 & 15 of the information handbook, available on the link shared below:

https://www.amrita.edu/print/information-handbook-btech-admission-2019