Hello there, online_payroll_user.
Thank you for posting in the Community. I'm here to provide information about your payroll concern in QuickBooks Desktop.
I need to ask some questions to make sure I can answer them thoroughly. Can you confirm if you're trying to migrate payroll data from Online to the Desktop version? Any additional information you could provide would be a great help.
There are export limitations when exporting transaction data to QuickBooks Desktop. Paychecks turning to regular checks is one of it.
For more information about what happens to your payroll information, you can visit this article (scroll down to Payroll Information):
Export limitations - QuickBooks Online to QuickBooks Desktop.
To record prior data, you'll need to enter the year-to-date amounts with a Desktop with a payroll service.
I look forward to your response concerning your payroll data. You can post a comment below, and I'll be sure to get back to you.