Try below code to load product collection by category id
$category_id = $this->getRequest()->getParam('cat'); // 10 as Category Id
$products = Mage::getModel('catalog/category')->load($category_id)
->getProductCollection()
->addAttributeToSelect('*')
->addAttributeToFilter('status', 1)
->addAttributeToFilter('visibility', 4)
->setOrder('price', 'ASC');