Force Movement on a Path with Path Switching?

Hello Unity Community, I am pretty new to Unity and Programming in general so i thought i would ask for help here. My Idea is to let a Square follow a line vertically. There are 3 Lines vertically. Vertical movement is solved trough a simple transform.Translate script. Now to horizontal movement, the square should be forced to follow a path, there should be no free movement and if the player touches either the right or left side of the touchscreen the square should jump to another Line and stay on there until the player touches a side again. My Questions are, how can i force the Square to stay on the Lines? and How do i force the square to jump the lines when the player touches?