I actually didn’t get you want single value from particular record or minimum date from whole list of records.
get_min_date = frappe.get_value(DocType, {"student_group": self.student_group}, ['schedule_date']) // For single record only
get_min_date_list = frappe.db.get_all(doctype, filters= { "student_group": self.student_group }, fields= ['schedule_date']) // From list of records
min([i.get('schedule_date', '') for i in get_min_date_list])