Which method in PowerMock-Mockito java can be used to replay the class under test (like PowerMock.replay() followed by PowerMock.verify()) and verify whether the private methods (methods are part of class under test ) calls ?
Solution
You shouldn't be verifying private method calls, as they're implementation details. That PowerMock allows you to do so is no indication that you should.
Even if you do choose to mock private method calls, you could only access them from your system-under-test, which indicates that you're mocking the system under test: Don't mock the system under test. It's far too easy to accidentally verify that your mocking system works, not that your component actually does what it's supposed to.
Mockito doesn't have record-replay semantics, so you won't be able to access that functionality from PowerMock-Mockito. You'd need PowerMock's EasyMock syntax instead.