Currently, there is no standard built-in Trial Balance by Class Report in QuickBooks Online. There is no way to customize from existing Trial Balance report.
You can run the Balance Sheet by Class (less Net Income line) and Profit and Loss by Class. Export it to Excel and merge it together.
That combined adjusted numbers distributed by class should be the same as the numbers in Trial Balance by Class if available.
If you think you need this feature added to future revision, you should send them your feedback to Intuit developers. You can create an “open customer feedback request” case from this Intuit website. This way other QBO users can also add valuable comments to your request. You can also review and vote on what other QBO users are asking for from here. http://feedback.qbo.intuit.com/
What’s on our feature request radar in QBO?
Many of our dedicated QBO users are asking for running balance in check register be a fixed permanent feature. You can also help by adding your Vote.