Great to see you here in the QuickBooks Community. I'd be happy to help share the steps how you can generate the report that you need.
You can customize the Job Progress Invoices vs. Estimates report to show the paid amount against the estimate, what is still open and what is left to be invoiced. However, it won't show the paid amount date against the customers' invoices.
In the meantime, you can enter a memo on the invoice, estimate, and payment for you to easily identify in which transaction it's against.
From the Reports menu, select Jobs, Time & Mileage.
Select Job Progress Invoices vs. Estimates.
At the top left, click the Customize Report button.
Click the Display tab.
Type Open Balance and Memo in the COLUMNS section, then put a checkmark beside them.
Click the Filters tab, then type Transaction Type in the CHOOSE FILTER section.
Click the Transaction Type drop-down, then select Multiple Transaction Types.
In the Select Transaction Types window, select Invoice, Estimate, and Payment.
Click OK twice.
You can also memorize this report to save its customization. Feel free to read these article for the detailed steps:
Is there a report showing the paid amount to date against my customers' invoices?
I have noted a QuickBooks Online report above. I just realized that the question was specific to the desktop version of QuickBooks. There are multiple way to customize payment reports in the desktop version using the customize report feature.