What type of exception in Java cannot be handled?

Error.

Error and its subclasses represent serious problems that a reasonable application cannot recover from. Examples include OutOfMemoryError, StackOverflowError, VirtualMachineError. They indicate failures at the JVM level or system resources that the application cannot fix on its own. Attempting to catch and handle them is ineffective and may even hide the true cause of the problem. Unlike RuntimeException or Checked Exception, which can be handled (caught or declared in the method signature), Error usually signals a fatal failure.