If we have a conducting disk (with constant electric potential = V where V > 0) and we divide disk as shown in attached file, where distance between two subdisk is equal, is it possible to have total negative charge over some subdisk in static case?
It is a circular disk. It is positively charged to V. Charges have mutual repulsion. They repel each other and tend to get distributed on the disk. Convex regions or sharper edges will have stronger charge (higher surface charge density). Thus all the positive charge will get distributed according to what is said. Thus the question of negative charge does not arise.