To create a new page with products have special price only, you need to create a new block that filters discounted products. 

Let’s create this file, Special.php in local/Mage/Catalog/Product/Block/ directory. You will have to create this directory path if it’s not already there.

Using below code to create new block 

<?php
class Mage_Catalog_Block_Product_Special extends Mage_Catalog_Block_Product_List
{
    protected function _getProductCollection()
    {
        if (is_null($this->_productCollection)) {
            $categoryID = $this->getCategoryId();
            if($categoryID)
            {
              $category = new Mage_Catalog_Model_Category();
              $category->load($categoryID); // this is category id
              $collection = $category->getProductCollection();
            } else
            {
              $collection = Mage::getResourceModel('catalog/product_collection');
            }
             
            $todayDate = date('m/d/y');
            $tomorrow = mktime(0, 0, 0, date('m'), date('d')+1, date('y'));
            $tomorrowDate = date('m/d/y', $tomorrow);
             
            Mage::getModel('catalog/layer')->prepareProductCollection($collection);
            $collection->addAttributeToSort('created_at', 'desc');
            $collection->addStoreFilter();
             
            $collection->addAttributeToFilter('special_from_date', array('date' => true, 'to' => $todayDate))
                ->addAttributeToFilter('special_to_date', array('or'=> array(
                0 => array('date' => true, 'from' => $tomorrowDate),
                1 => array('is' => new Zend_Db_Expr('null')))
                ), 'left');
             
             
            $numProducts = $this->getNumProducts() ? $this->getNumProducts() : 0;
            $collection->setPage(1, $numProducts)->load();
  
            $this->_productCollection = $collection;
        }
        return $this->_productCollection;
    }
}