How can we implement search  for specific list in sitepage in sharepoint 2013?
you can use the Content Search Web Part and set it to only return results from a specific list. There is a good tutorial at http://blogs.technet.com/b/tothesharepoint/archive/2013/04/30/stage-9-configure-the-query-in-a-content-search-web-part-on-a-category-page.aspx