how can i lock y position of a player when its being dragged?

i want to be able to drag my player over X axis and Z axis, like if it were sliding over the floor, but when i move it on the Z axis, because of the camera's position (orthographic and the ground looking like this a rhombus) when i drag the player through X axis it slides well over the ground, but on X axis it also goes uppwards, moving in a diagonal line that its center is the center of the ground.

here is my script:

using UnityEngine; using System.Collections;

public class drag : MonoBehaviour {

 public Player player;
 float distance = 10;
 void OnTouchDrag(){
     Vector3 mousePosition = new Vector2 (Input.mousePosition.x, Input.mousePosition.z, distance);
     Vector3 objPosition = Camera.main.ScreenToWorldPoint (mousePosition);
     transform.position = objPosition;
 }
 void FixedUpdate()
 {
     if (player.transform.position.y != 0)
     {
         transform.position = new Vector3(0, 0, 0);
         print(transform.position.y);
     }
 }

}

here is an image of the scene before: https://snag.gy/4hyMWV.jpg here is when i move it over the Z axis: https://snag.gy/xe8jNb.jpg and here is when i move it over the X axis: https://snag.gy/VR0TWH.jpg and again, when i move it over the X axis towards the other side: https://snag.gy/S94DaV.jpg

It seems its for some reason moving on the Y axis too, but i cant lock Y axis if im dragging the player :( please, i need help pretty urgent :( thank you a lot by the way.