Can Banks refuse a legal Power of Attorney from authorized party?

Can Banks refuse to honor a legal Power of Attorney from authorized holder trying
To transact legitimate banking business?

They will need to be presented a copy of the POA and have time to verify it if needed by their rules.

Who is holder and what is the legitimate banking business? Is this an offshore type of deal? To answer your question, with just what you wrote, is not quite possible. You left out some important details.