1

using UnityEngine;
using System.Collections;

public class ClickButton : MonoBehaviour {
    public string Previous = "";
    public GameObject PopUp;

    void OnMouseDown()
    {
        Destroy(GameObject.Find(Previous));

        Instantiate(PopUp);
    }
}

Everytime I run and click on the button the clone object stays and instantiates the new object however if the object is not a clone it works fine. However it being a clone is necessary

2

Hm, I believe that might be because cloned objects usually have a name like “PrefabName (Clone)”, perhaps. You usually would have to set the name of the cloned objects directly, like, newObject.name = Previous.
Could you see what the name of the instantiated objects are?