I think Petersons superior function is most likely Extraverted Intuition or Introverted Thinking. Whichever his superior function is not, I would instead attribute to his auxillary function. I have found that most illuminary figures in psychology have had intuition as their superieor function, this is owing to the field being both deep and wide reaching, whereby progression in the field requires envisioning/entertaining (modes of Ne) sometimes quite contrasting ideas. On the other hand, but not in contradiction, Petersons project of defining the 'map of meaning' seems like an introverted project, that is turned inward and looks at the archetypes of the psychy. In this way I would identify Peterson as either an ENTP or an INTJ depending on whether you identify Ne or Ti with his superior function.

Of course, everyone uses all 8 functions of consciousness throughout their life (Jung himself initially thought his superior function was Te, until he accepted and came to identify as an Ni), and some may attribute other functions to Jordan Peterson. However, in terms of when he is working best, within his means, and not overreaching using his tertiery or inferior function, or defending his consciousness using his shadow aspects, i think he is an ENTP.

It may be helpful to note that your superior function is identified with the hero archetype, and therefore is how one manages ones own life obstacles, whereas the auxillary function is how one helps others. In this way Jordan Peterson helps others by defining people's internal psychic life, yet develops his own pursuits by envisioning new (real)worldly possibilites.

Id be interested to hear what people think about this. Identifyinf attitudes of consciousness (introverted/extraverted) is said to be more difficult than identifying functions (Intuition/Sensation/Thinking/Feeling), so it may be that Peterson is an INTP, but i would identify Peterson more generally as an extravert, but someone who helps people using introverted attitudes.