1999 Lincoln Continental stheering wheel shakes

Can you be more specific? A lot of different symptoms can be referred to as "jumping". Does the car have to be moving? Do you see the steering wheel move left and right while you're driving slowly through a parking lot? How does it steer on the highway?

When I put the car in gear the steering wheel pulses left to right while turning the car to the right or to the left but not when going straight

This is best handled with an inspection at a tire and alignment shop. A broken belt in a tire can cause this but you'd feel that when going straight too. Same with a bent wheel. I suspect there's an issue with the power steering pump, (weak output), a loose drive belt, or something like that. There can be internal leakage inside the steering gear too, but to affect steering in both directions is not common.

I believe it is the belt when I inspected the belt I was able to pull from under the top idler pulley with my hand without releasing the tension off of it I guess the is why my battery will not keep a charge the belt did not have any cracks in it well I am going to run and purchase a belt to install on the car and pray that it will take care of the issue thanks

Check for a spring-loaded tensioner pulley. Sometimes they rust in the pivot bolt and don't provide enough tension on the belt.