Does a baby necessarily have mothers or fathers blood group?

The same blood flowing in the body of the mother, flows in the child. So the mothers.

As to the bloodtype it will have its own, either the same as one parent or a combination of the two. Mothers with negative blood who have children with positive blood are at greater risk of having a miscarriage.

The Mothers blood NEVER comes in direct contact with the developing baby. The mother's blood supplies nutrients to the placenta which transfers nutrients (and oxygen) to the baby's blood.