There are not e-file fees when using the TurboTax online editions, federal or state.
There is a $50 charge for use of the state program software when using the Premier online edition.
Go to this TurboTax website for the online editions and click on the link State additional - https://turbotax.intuit.com/personal-taxes/online/
In the Online versions Deluxe and above each state is $50. If you want to have the fees deducted from your federal refund there is an EXTRA $40 Pay with Refund Service charge you can avoid by paying with a credit card.
How to see your fees
https://ttlc.intuit.com/community/charges-and-fees/help/how-do-i-review-my-fees-in-turbotax-online/00/26353
For help with fees
https://ttlc.intuit.com/community/charges-and-fees/help/what-can-i-do-to-reduce-my-fees/00/26051
How to remove the Pay from your Refund fee
https://ttlc.intuit.com/community/downgrading/help/how-do-i-remove-pay-with-my-refund-fees-in-turbotax-online-and-change-my-payment-method/00/25880