How often should I replace my transfer case fluid has 120000mi. how much $

Always good to change fluids in all lubricated areas before 100,000 miles. The fluids are the life blood of your moving components. Depends on your driving conditions, but I change mine every 50,000 on differentials, 40,000 on automatic transmission. Your transfer case only takes 1qt of gear oil, and only takes a few minutes to drain and refill. No Worries.

I don't see any manufacturers recommendation for a service interval. There are ,however, intervals for inspecting the fluid. I would have your shop explain why it should be changed and if youn don't trust their recommendation then you might want to find a new shop you do trust.