First, head to your project list and add your Custom Columns.
Then, add in 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.
From here, you can sort your project list by Billing Status by clicking the column header to show you all projects with a due balance at the top.
Finally, you can download your project list (or just those selected 'Due' projects) into an Excel Document for a summary for your client.