Drag Object with Mouse Along Y-Axis

I am trying to create a pong type game and I have ran into a problem. I want the player to be able to drag the paddle along the y-axis but the game object is not behaving the way I want it to. Here is my code:

    private Vector3 screenPoint;
    private float startPosX;
    private float startPosZ;

    void Update ()
    {
        startPosX = -10.0f;
        startPosZ = 0f;

        transform.position = new Vector3(startPosX, Input.mousePosition.y, startPosZ);
    } 

    void OnMouseDown()
    {
        screenPoint = Camera.main.WorldToScreenPoint(gameObject.transform.position);
    }

    void OnMouseDrag()
    {
        Vector3 currentScreenPoint = new Vector3(startPosX, Input.mousePosition.y, screenPoint.z);
        Vector3 currentPos = Camera.main.ScreenToWorldPoint(currentScreenPoint);
        transform.position = currentPos;
    }

I only want the paddle to move along the Y-Axis but it seems that when I try to drag the object it suddenly appears off the game screen. Is there another way to do something like this? Or am I doing this wrong?

I think when you are setting the position in Update, you should change your y-Coord to Camera.main.ScreenToWorldPoint(Input.mousePosition).y, as this would convert the y position of the mouse in Screenspace, to the y position of the mouse in WORLD space, which is what you want