Are the jinn subservient to humans, and what is the Shari’ah ruling on that?

There is no evidence that jinn are subjugated to serve humans, but jinn, or some of them, may be subjugated to some human beings. The relationship between jinn and humans takes several forms:

One who commands jinn in accordance with what Allah and His Messenger have commanded is among the best of Allah's awliya (saints/friends).

One who employs jinn in permissible matters, just as one would employ humans in permissible matters.