[CODE]Keep Gameobject position exactly at mouse cursor when cast float position to int

Hey everyone! I'm creating a 2d top-down game and currently im working on a script which should keep the Gameobject position exactly at the same position of the mouse, but it doesn't work. Maybe it's because I'm casting a float to an int, but I have seen other games where it works very well.

Problem: When I move the mouse very fast the object glitches from it's position

I hope anyone can help me!

 void Update ()
     {
         mousePos = Camera.main.ScreenToWorldPoint(Input.mousePosition);
 
         yMin = (int)playerRectAncor.transform.position.y - 1;
         yMax = (int)playerRectAncor.transform.position.y + 1;
         xMin = (int)playerRectAncor.transform.position.x - 1;
         xMax = (int)playerRectAncor.transform.position.x + 1;
 
         if (true) //Its just temporary true, for testing
         {
             pos = Camera.main.ScreenToWorldPoint(Input.mousePosition);
             pos.z = transform.position.z;
             pos.x = Mathf.Clamp(pos.x, xMin, xMax);
             pos.y = Mathf.Clamp(pos.y, yMin, yMax);
            // put Object position to mousePosition
             rectObj.transform.position = new Vector3((int)pos.x, (int)pos.y, (int)pos.z);
         }