how to verify a method of a non-mock object is called?

It seems mockito only verifies whether a method of a mock object is called and the mock object always have something like doReturn().when(mock object)

But can I create a mock object and define doReturn().when(mock object) and then verify a method of another object is called?

Here is what I want to do: I define a mockEnvironment and return a response no matter what happens. But then I want to verify different methods of anotherObj is called in different cases.

How to do that?

public class BaseClass {
    private Environment mockEnvironment;
    @Test
    public void testcase () {
     setMockitoEnvironment(); 
     response = foo(mockEnvironment, argument1);
     verify(anotherObj).codePath1(...);
     response = foo(mockEnvironment, argument2);
     verify(anotherObj).codePath2(...);
   }
}

//this method successfully return a response with any input 
//because I do not care how response is eventually generated, 
//I only care whether code path reaches createResponse() via 
//code path 1 or code path 2.
private void setMockitoEnvironment() {
    mockEnvironment = mock(Environment.class);
    doReturn (response).when(mockEnvironment).createResponse(for any input);
}
private Response foo(...) {
    ... 
    return createResponse(...);
}

You can use a Mockito Spy for this. If you setup anotherObj as a spy you can verify method calls on that object. In your example you need to make sure that the call to foo uses the spy instead of an ordinary implementation of anotherObj. The spy is setup something like this:

AnotherClass anotherObjSpy = Mockito.spy(new AnotherClass());
// do stuff -- e.g. anotherObjSpy.foo(...);
verify(anotherObjSpy).codePath1(...);

Annotate the non-mock object with @Spy annotation and then check for verify(). Check this