Add tag parameter to category.php

This is an old plugin, but I think you will get idea from this plugin

Similar thing is possible with this plugin, you will find more details in plugin description.

Alternatively you can use “pre_get_posts” action in your theme’s functions.php file to call only on category archive page using below code. Below code will add filter on the category.php page to fetch posts with tag ‘red’.

function tag_filter_category( $query ) {
if ( is_category() ) {
   $query->set( 'tag', 'red' ); // to fetch posts with tag red (color)
  }
}
add_action( 'pre_get_posts', 'tag_filter_category' );