If you have sent a Contact an Invoice you make a partial payment against that invoice quickly.
Head to Finances > Invoices, Expenses and Deposits
Select Awaiting Payment and then Number to display the outstanding invoice.
Click Add Payment.
Register the details of the part payment. Untick the Pay in Full option to edit the amount paid. You can also choose to send a Receipt to the Payee of the transactions if you like.
Your Finances will all be updated and the Amount Due to you will have been reduced. You can choose to send them a payment notification email and also a new reminder.