In the court - in the place called the court (which needn't be a court of law - we often refer to courtyards as courts).
I've never heard anyone say I'll meet you in the court in a legal context. It's the sort of thing students say to each other in ancient universities.
See you in court is what people say when they are going to law and their adversary starts trying to resolve the case beforehand. It often means I'm not prepared to discuss this any more. I think I'm right and am prepared to let the court decide.