Money "Paid Out" should match any receipts that are in the register.  And at any point in the day the total of the Cash Drawer should equal Cash you started the day with + Sales - Paid Out Receipts

So in theory you could have started the day with $200 in the Cash Drawer, had $100 in Cash Sales and paid this vendor $50.  So your Cash Drawer at the end of the day would have $250.  Your Z-Tape should show the $100 in Sales and $50 paid out, so you're in "Balance" at the end of the day.  So that's it with the Z-Tape, right?

But that Paid Out receipt now needs to make it into QBs.  It's not a Sale or Return, so it does not have anything to do with your Sales Accounts.  It was a flat out Expense and you need to show it in QBs the same as you normally would - except that it was paid for with Cash. 

So as I said, you can enter the Receipt/Invoice into Bill Pay if that's what you usually use and then go to PAY the bill as you usually would, but be sure to use your CASH Account, NOT Checking since it was not paid with a check or Debit Card.

If for any reason you do not use or want to use Bill Pay for this, then go directly into your Cash Account Register and enter the Vendor, amount and correct Expense Acct to make sure the Expense is properly shown in QBs. 

At the end of the day the total shown in your Cash On Hand Account should equal whatever Cash you started with (Cash Drawer, a safe, an envelope in the office if somebody needs to make change or whatever) PLUS whatever Cash Sales you made that day LESS the payment (or payments) you made in Cash.