Quickbooks Online is assigning bank deposits to open invoices randomly. Can I stop this from happening?

Let's make sure that the payments are attached to the correct invoice, arthur-podell.

Can you also tell us how was the payment recorded in QuickBooks? Was it made by the Receive Payments option? If so, you actually need to click the drop-down list for the Deposit to field and select the correct account. 

If you're referring to applying it to the correct transaction, select which open invoice in the Outstanding Transactions section. This way, the payment will be applied to the correct one (see attached screenshot). Let me share these articles for more details:

• Record invoice payments in QuickBooks Online
• Record and make Bank Deposits in QuickBooks Online

You can also run the Invoices and Received Payments report. This will tell you the payments you’ve received and the invoices that go with them. Just go to the Reports menu and look for Invoices and Received Payments.

Keep me posted if you have follow-up questions. I'll be around to help you again.