[ITask][1] and [ICase][2] implements the [INoteable][3] interface. So normally it doesnt doesn't make sense to persistent persist notes on a DataClass. But you can manage the notes of the actual user task or process instance (case).
[1]: http://developer.axonivy.com/doc/latest/publicApi/ch/ivyteam/ivy/workflow/ITask.html
[2]: http://developer.axonivy.com/doc/latest/publicApi/ch/ivyteam/ivy/workflow/ICase.html
[3]: http://developer.axonivy.com/doc/latest/publicApi/ch/ivyteam/ivy/workflow/INoteable.html