It seems you're using QuickBooks Online, Will K.
The payments that are not deposited to the bank account yet will show as "Not Deposited".
You can check the screenshot below.
If you have other questions, just tag me and I'll get back to you personally.
I didn't word that well, half addressing two different questions.
1. Does the deposit or received payment change cash basis sales?
the next is about what you pictured
2. Which clears the overdue/unpaid?
I think the issue I'm having with this part is partial payments or payments not applied to an invoice.
Hello there, @Anonymous.
Thank you for getting back getting back with me. I'd be happy to help share some information about receive payments.
Let me address your concern one by one. To answer your first question, yes, when using the Cash sales accounting, income and expenses affect the report at the time you receive a deposit or payment. It doesn’t matter whether the payments have been deposited to the bank account or not.
Next, to clear an overdue/unpaid invoice, you need to record the full payment. When you save a partial payment, it only reduces the balance due on your invoice however the status is the same. The overdue/unpaid status will only be lifted once the payment is complete.
However, if you're referring to the customer payments that were entered through the Make Deposits screen and are not connected to an invoice, you need to link the deposit to the customer payment to clear them.
The steps below are for QuickBooks Online.
To start, let's find the deposit, here's how:
After that, let's link the deposit to the invoice.
These steps will guide you to make the invoice marked as paid. I've added this article for your future reference: Linking a Deposit to an Invoice.
If you're referring to something else or product, let me know. I'm just a post away.