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

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(...);