Pause Button on iPhone

I got my pause button working fine in Unity on my iPhone. But the problem I am having is that when the user touches the anywhere on the screen, the character jumps, but when the user presses the pause button, it pauses the game but also causes the user to jump. So when the unpause it, they fall to their death because it had jumped for them.

So disable the jump script. Or in the jump script check if the game is paused, and only jump if it is not paused.

That wont work because as the player presses the pause button, it jumps and then is instantly paused. It appears as if he hasnt jumped but as soon as the play button is clicked, he resumes his jump that was started when they paused the game.

You need to check where the player is touching on the screen.
If you manage the jump using a simple input.TouchCount > 0 then jump, your character will always jump whenever the screen is touched, so also when you touch the pause button.