Coordinates of mouse in a box collider

If your camera is axis aligned, and you know the world size of your object and your world object is not scaled, then calculating the relative x-axis is fairly straight forward. If your camera has a rotation of (0,0,0) and is therefore looking towards positive 'z', you can add a script like this to the object:

 var pos = Input.mousePosition;
 pos.z = transform.position.z - Camera.main.transform.position;
 pos = Camera.main.ScreenToWorldPoint(pos);
 pos = transform.InverseTransformPoint(pos);

'pos' is now in local coordinates. Negative values will be to the left, positive to the right. You can set a threshold for what you consider 'middle'.