Hello,

yes you are eligible as your parents must be a resident of bihar and you are a minor so you will get the domicile certificate.

there are some rules by bihar government to be eligible for domicile certificate Those are:-

1. applicant must have lived for past 3 years
2. applicant must have owned any property
3. applicant must have name in voter list
4. if minor then apply using parents residence basis

so you go in minor category. if your parent satisfy any one of above 3 then you can apply for domicile certificate and use home state quota for admission.

here is the link for NIT campus cutoff:-

https://engineering.careers360.com/articles/nits-cutoff-for-top-btech-branches

Hope it helps!