Filter posts in a query if they have only one certain tag

Try adding HAVING condition between GROUP BY and ORDER BY:

...GROUP BY wposts.IDHAVING COUNT( tag_terms.term_id ) <> 1  OR MAX( tag_terms.term_id ) <> 55ORDER BY wposts.post_date ASC

and change your WHERE condition to check only for post type and status.

Also if you don't select anything other than tag_id from wp_terms joining it is not necessary as you can just use term_id from wp_term_taxonomy.

If you want all the posts with a certain tag, then why have you specified the post ID in the query ?

This following query will show all posts with the given tag id

SELECT wposts.ID AS ID,wposts.post_title, wposts.post_status, wposts.post_name,tag_terms.term_id AS tag_idFROM `wp_posts` AS wpostsINNER JOIN wp_term_relationships AS tag_term_relationships ON (wposts.ID = tag_term_relationships.object_id)INNER JOIN wp_term_taxonomy AS tag_term_taxonomy ON (tag_term_relationships.term_taxonomy_id = tag_term_taxonomy.term_taxonomy_id AND tag_term_taxonomy.taxonomy = 'post_tag')INNER JOIN wp_terms AS tag_terms ON (tag_term_taxonomy.term_id = tag_terms.term_id)WHERE wposts.post_type = 'post'AND wposts.post_status NOT LIKE 'private'AND tag_terms.term_id = '55'GROUP BY wposts.IDORDER BY wposts.post_date ASC

Now, if you want to make sure that these posts have only the given tag id, nest the query as follows :

    SELECT wposts.ID AS ID,    wposts.post_title, wposts.post_status, wposts.post_name,    tag_terms.term_id AS tag_id    FROM `wp_posts` AS wposts    INNER JOIN wp_term_relationships AS tag_term_relationships ON (wposts.ID = tag_term_relationships.object_id)    INNER JOIN wp_term_taxonomy AS tag_term_taxonomy ON (tag_term_relationships.term_taxonomy_id = tag_term_taxonomy.term_taxonomy_id AND tag_term_taxonomy.taxonomy = 'post_tag')    INNER JOIN wp_terms AS tag_terms ON (tag_term_taxonomy.term_id = tag_terms.term_id)    WHERE wposts.post_type = 'post'    AND wposts.post_status NOT LIKE 'private'    AND tag_terms.term_id = '55'    GROUP BY wposts.ID    HAVING COUNT( tag_terms.term_id ) <> 1    OR MAX( tag_terms.term_id ) <> 55        ORDER BY wposts.post_date ASC