did your father take migration to chattisgarh by seeking domicile in chattisgarh? if not , the chattisgarh authority of ST board may not accept ST position for your father; but your mom shd be having i think if she is an ST. then claim her ST position as these days mother's name as important as father's position, so your school would carry your mom's name too, that route might perhaps help you to claim ST classification.
Pls note there is straight procedure that one can be said one belongs to one community when one of the spouses migrates to new state.
India suffers from improper classifications of 'sur names' on one's name; but that must have been done by the government of India. another problem when 'dalit' is further added to one's name that created further problem. as 'dalit' need not be just from ST or SC only as any one can become a 'dalit' (just it denotes the person is a buddhist only , nothing more). so dr B R Ambedkar did not ablish all sub castes and brought all f them together under one classification, that is the problem, today SC and ST face problems. so also in OBC, BC classifications.
Besides there is no hard and fast rule of any 'caste classification' as such, except one what he or she calls himself or herself, this kind of problem is only encouraging all kinds of corruption in certification today.
So far none moved the courts in the right direction.
Your option is just claim your mother's caste as she is from chattisgarh, being very native, with some local caste classification, that way you can succeed; don't press here your father's caste classification of Jharkhand, fot it is already rejected. tks.
