Not sure what you mean here. I pay no fee, not even a penny, for debit transactions of any kind. I use a small Credit Union, for what it's worth.
As far as the vendor is concerned, the cigar shop I frequent prefers you pay by debit, as opposed to credit, if given the choice. I forget if they pay a lower fee, or if they get their money quicker, when the customer chooses "debit". Either way, I am only charged the amount of the sale.