You would share DNA with both A and B because they have the same grandparents since A's father is B's sister
If A is your half-sibling then B is your cousin through your natural father's parents (your natural grandparents).
I.e. Mr and Mrs X had two children: John Doe and Jane Doe.
You and A are the children of John Doe. B is the child of Jane Doe.
Therefore B is your cousin.