A school affiliated to some board like CBSE does not allow private students or any provision like that. Your school will not allow that , you van confirm it by yourself. If you want to appear as a private student then there is a provision of open school, but in that case you won't have anythonh to do with your school or any of its recognition. If you want your school's recogntion then only way is to join your school as a full candidate.

All the best.