Could you elaborate? I didn't fully understand. What do you mean by objects conforming or not conforming to our cognition?
All experiences seemingly derived externally are perceived through the senses and organized through what is called cognition. We can call those externalities perceived objects, and here it is important to note that objects can be concrete and abstract. Perception is made up of sensory data that is filtered through the senses and organized into an object through cognition.
There is not much question of how we receive the object, the question is more what the objects nature is and what can be said about it. We can not say with any confidence that we know a thing in itself and instead can only know its appearance and what it represents. The former is the actual externality we want to know while the latter are the objects we perceive.
If cognition conforms to objects, then we can only know their nature in so far as our cognition conforms to their nature. That is we can only know a thing in itself in so far as are cognition is capable of representing a thing in itself. If objects conform to our cognition, then we can only know their nature in so far as that nature conforms to our own. That is we can only know a thing in itself in so far as it representable.