PAYROLL TAXES

Where your employees live and work determines the state payroll taxes you and your employees are subject to, TRAL23.

I suggest reviewing your employee's setup to see if someone worked or lived in Arkansas. That is why the system prompts you to enter an address in Arkansas, though your business isn't there. To do so, you can go to the Reports menu. Then type and choose Employee Details report. Refer to the screenshot below for visual reference:

If you need to edit your employee's location, here's how:

1. Go to Payroll, then Employees.
2. Select your employee.
3. From Tax withholding, select Edit.
4. In the Local Taxes section, select Edit location. Enter the city and ZIP code combination for the local tax jurisdiction you need.
5. Tick Save.

Additionally, some states have reciprocity agreements, which means employers may be required to file and pay taxes for each state, even if the business and employees are in different locations.

To help you when you need to take a closer look at your business and payroll information, I've added this article for your reference: Run payroll reports in QBO.

Notify us if there's anything else we can help you with. Comment below if you have more questions about managing your payroll taxes within QuickBooks. We'll be happy to assist you further.

@AdonL  RE: I’d be glad to provide some details on why QuickBooks is prompting you to finish the payroll setup for Arkansas, TRAL23.

Does that answer the OP's question? No it does not.

Did you in any way answer the OP's question? No you did not.

The question is how can the OP sign up for an account in Arkansas, which QuickBooks is pushing them to do, when it (QuickBooks?) requires an Arkansas business address and they don't have one?  It's a simple question. Not at all complicated.