Which is the rarest blood type among these?

AB negative, at well under one per cent of most populations - though rarest depends entirely on where you are asking. Blood group frequencies vary enormously by ancestry: type B is far commoner in South and East Asia than in Western Europe, and type O is close to universal among indigenous populations of South America.

The genuinely rare types are not in the ABO system at all. There are more than forty other blood group systems, and the rarest known is Rh-null - people with none of the Rh antigens whatsoever, sometimes called golden blood, of whom fewer than fifty have ever been identified. It can be given to anyone with almost any rare Rh type, which makes it enormously valuable, and the people who have it can receive only from each other, which makes their own position precarious.

That precariousness is the practical problem. A person with a rare type usually banks their own blood before planned surgery, and international registries exist to move units between countries for individual patients. There is a small permanent network of donors, some of whom have been giving for decades for the benefit of people they will never meet, and whose type is rare enough that they are effectively irreplaceable.