Domicile certificate is a certificate issued by the authority of your state that proves that you belong to the state or you are the domicile of the state. And category certificate proves that you belong to a particular backward category, and you need reservation for taking admission in colleges because of your inability due to caste. So in case you have applied through any category, you need to show the certificate and exam conducting authorities need to verify that. So they have to Check if the certificates are valid. All the best!