In QuickBooks Self-Employed, you can apply the overpayment for future invoices of your customer, you can add another line item and enter it as a negative amount (overpayment). This will deduct the total amount that your customer is obliged to pay. Here's how:
Go to Invoices on the left panel.
Click Create Invoice.
Enter all the required details.
Add another line item for the overpayment.
Click Save.
Here's a sample screenshot:
For the invoice where the overpayment is applied, you can open it and add a note that this transaction has an overpayment amount in the Note to Customer field. Go to the Invoice lists and select Edit under the Action column.
Also, you can manually add the partial payment. If you need more information about it, you can check and read through this article: Manually add transactions in QuickBooks Self-Employed (QBSE). When it's fully paid, you can mark the original invoice as paid.