If you chose to pay your TurboTax fees out of your Federal refund, and if your Federal refund has been delayed unusually long at the IRS (or if it's been reduced), TurboTax will want to be paid. They likely started sending you emailed bills to pay. If you didn't respond by either paying or asking for a deferment, they would ultimately debit your bank account. If you didn't get the emails, check other email accounts and also the spam/junk folders.
See this FAQ that explains the process. The first paragraph has a special phone number if you have a question or need to appeal a NSF fee (non-sufficient funds/overdraft fee).
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FAQ: Why was my bank account auto-debited for the TurboTax fees?
Your state tax due cannot be paid from your federal refund.
It is not possible to pay your state tax due from your federal refund, nor is it possible to pay a federal tax due from a state refund. The federal and state treasuries are completely separate from each other. You may have seen a TurboTax summary of your federal and state amounts that confused you into thinking one was “paying” the other. It is not. If you have federal tax due you can pay by mailing your payment, having the payment taken out of a designated bank account, or you can pay directly on the IRS website. You must pay your state tax due using the state’s preferred method of receiving payment. For most states that will be by making a payment to the state’s own tax website, or by mailing a check or money order.