Florida has no state taxes for filing and I did not work in NY, so my refund says 0 for NY state taxes. Why am I being charged an extra $34.99 on top of the $54.99?

How does NY enter into this?

The amount of $34.99 is not for a state tax return when using the online Deluxe edition of TurboTax.  A state program using Deluxe would have been $39.99.  Click on State additional under the Deluxe edition on this TurboTax website - https://turbotax.intuit.com/personal-taxes/online/

You must have requested to have the optional Refund Processing Service ($34.99) to have your TurboTax account fees deducted from your federal tax refund.  See Screenshot

Additionally, if you have NOT filed your 2016 online tax return and you do NOT want to have the TurboTax account fees deducted from the federal tax return, preferring Now to pay the fees with a credit or debit card, then see this TurboTax support FAQ on how to remove the Refund Processing Service - <a rel="nofollow" target="_blank" href="https://ttlc.intuit.com/questions/1900517-how-do-i-remove-the-refund-processing-service-and-change-my-payment-method-to-credit-or-debit">https://ttlc.intuit.com/questions/1900517-how-do-i-remove-the-refund-processing-service-and-change-my-payment-method-to-credit-or-debit</a>