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Conclusion is that custom field options present in e.g. a drop-down menu will be copied to its cloned version, however a context applicable for particular, original scheme will not be copied. Cloned custom filed will remain with the same options and can be used for different project's issue type(s) where all of its elements remain intact, just as in its original form:
As you can see field named "Device Selection COPY" is present right now in selected Project and Issue Type.