Government aided teacher are group b government employees or not

A teacher working in a government-aided school is generally not considered a Group B officer; in most cases, they are not considered government employees at all, as the school is privately managed even though it receives government aid, placing them outside the official government classification system of Group A, B, C, and D officers. 

A aided school teacher is not a Government employee. As such, there is no question of them being belonging to any group?

Yes.  But in Andhra Pradesh, the aided teachers are now absorbed into Government.  So verify in your state as the government makes decisions on the circumstances of the state