Unity3d Dragging object in 3d world

Hello, I am new to Unity. I have a 3d object (a prefab with a Mesh Renderer, Box Collider, and Rigid Body) that resides on a cube (also has Cube (Mesh filter), Box Collider, and Rigid Body).

I have code the instantiates the prefab onto the Cube. This works fine. I now want to drag the prefab along the top of the cube, so the user shouldn't be able to drag the prefab up, away from the Cube, only move it along 2 dimensions.

Attached to my prefab, I have a script, for dragging. The script allows for dragging, but it will not keep it on the 2d plane, which is the top of the cube. How can I achieve this? I've tried freezing the Y position, on the prefabs Box Collider, but all this does is freeze the prefab in what ever position it is dragged too.

This code sort of works but it does not hold the prefab onto the cube's top. As my game allows the camera to be rotated, you can rotate to a steep angle. Then, when you drag the prefab, you are still able to get the object to move on the Y axis.

Here is my code:

 public class DraggableObject : MonoBehaviour {
     public bool dragging = false;
     private Vector3 screenPoint;
     private Vector3 offset;
     private float originalY, orginalZ;
 
     float lerpTime = 1f;
     float currentLerpTime;
 
     float moveDistance = 10f;
 
     public Vector3 startPos;
     public Vector3 endPos;
 
 
     void Start()
     {
         startPos = transform.position;
         endPos = transform.position + transform.up * moveDistance;
         originalY = this.gameObject.transform.position.y;
         orginalZ = this.gameObject.transform.position.z; 
 
     }
     void OnMouseDown()
     {        
         screenPoint = Camera.main.WorldToScreenPoint(gameObject.transform.position);
         offset = gameObject.transform.position - Camera.main.ScreenToWorldPoint(new Vector3(Input.mousePosition.x, originalY, orginalZ));      
 
     }
 
     void OnMouseDrag()
     {
         Vector3 cursorPoint = new Vector3(Input.mousePosition.x, originalY, orginalZ);
         Vector3 cursorPosition = Camera.main.ScreenToWorldPoint(cursorPoint) + offset;
         transform.position = cursorPosition;
         dragging = true;
        
     }
 
     void OnMouseUp()
     {
         dragging = false;        
         endPos = transform.position;
         lerp();
     }
 
     private void lerp()
     {
         //increment timer once per frame
         currentLerpTime += Time.deltaTime;
         if (currentLerpTime > lerpTime)
         {
             currentLerpTime = lerpTime;
         }
         float perc = currentLerpTime / lerpTime;
         transform.position = Vector3.Lerp(startPos, endPos, perc);
     }
    
 
 }