After all researches, I made it. Like I have created a CMS page in CMS > Pages with content
{{block type="core/template" template="page/html/brands.phtml"}}
So the URL looks like.
https://magento.store.com/brand?q=fossil
For listing the products corresponding to brands
$brand = Mage::app()->getRequest()->getParam('q');
$productModel = Mage::getModel('catalog/product');
$attr = $productModel->getResource()->getAttribute("brands");
if ($attr->usesSource()) {
$brand_id = $attr->getSource()->getOptionId($brand);
//$brand_label = $attr->getSource()->getOptionText($brand_id);
}
$_productCollection = Mage::getResourceModel('catalog/product_collection');
Mage::getModel('catalog/layer')->prepareProductCollection($_productCollection);
$_productCollection->addAttributeToSelect('*')->addAttributeToFilter(array( array( 'attribute' => 'brands', 'eq' => $brand_id ) ))->addStoreFilter();
the above logic will find the attribute id first. Then it will add to addAttributeToFilter to find corresponding product collection. Then we can give the style to the listing.