First, head to your project list and add your Custom Columns.
I suggest Billing Status, Client Name, Due Balance, etc to make it easy for you to see these results.
Next, you can search your project list for that specific client. You can also Filter your project list to show you just projects with a Due Balance. (Article)
Finally, you can download your project list (or just those selected 'Due' projects) into an Excel Document for a summary for your client.