Right. So you got the partials folder, also using extension naming convention.. good. You don't need it for the partial tho, but it's still wrong. Why? You will need unescaped code, and pass it a JSON formatted data object, both are missing.
!= partial('slider_specials', { 'filter': 'special' } )
Something like that works for me with a file in partials/ named slider_specials.html.jade