How to add ModelState.AddModelError message when model item is not binded

The ModelState is created at each request so you should use TempData.

public ActionResult Delete(string id, string productid)
{             
    int records = DeleteItem(id,productid);
    if (records > 0)
    {    
        // since you are redirecting store the error message in TempData
        TempData["CustomError"] = "The item is removed from your cart";
        return RedirectToAction("Index1", "Shopping");
    }
    else
    {
        ModelState.AddModelError(string.Empty,"The item cannot be removed");
        return View("Index1");
    }
}

public ActionResult Index1()
{
    // check if TempData contains some error message and if yes add to the model state.
    if(TempData["CustomError"] != null)
    {
        ModelState.AddModelError(string.Empty, TempData["CustomError"].ToString());
    }

    return View();
}

RedirectToAction will clear ModelState. You must return a view in order to use this data. Therefore, the first if case won't work. Also, ensure that you have a control in your view (like ValidationSummary) which displays the error... this could be the problem in the second case.