The query of archive page is defined by wordpress, you do not need define it in the taxonomy-client.php file,
Please try this:
1) modify the first PHP codes you mentioned above as this:
function customize_customtaxonomy_archive_display ( $query ) { if (($query->is_main_query()) && (is_tax('client'))) $query->set( 'posts_per_page', '3' ); $query->set( 'orderby', 'title' ); $query->set( 'order', 'ASC' ); $query->set( 'post_type', array('photography') ); } add_action( 'pre_get_posts', 'customize_customtaxonomy_archive_display' );
2) save your default theme file archive.php as taxonomy-client.php, and customize it as what you want
If the problem still exists, please duplicate same problem in a test site, and fill below private details box, with the login details, I need a live site to debug