Post of a specific category – not to be seen in paging previous/next post

You should be able to exclude the category you don’t want to show by adding $excluded_terms to your navigation links. So for example, if the category you don’t want showing up is id 4 your link would look like:

<?php next_post_link( '%link', 'Next Post', false, '4' );?>

Same with previous_post_link().