Sitelink search box on and off

Sitelinks are automatically generated by Google based on your site structure and is not based on our plugin’s settings. Google is kind of tricky when it comes to Sitelinks. You can learn a little more about Google and Sitelinks here: https://support.google.com/webmasters/answer/47334?hl=en and this guide also explains more about Google Sitelinks: https://support.google.com/webmasters/answer/47334?topic=8523 .
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​However, you could signal to Google which ones you want to appear by using the following actions:
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Provide a clear structure for your website, using relevant internal links and anchor text that’s informative, compact and avoids repetition.
These guides explains more on the Site Structure of a Growing Blog: https://yoast.com/the-site-structure-of-a-growing-blog/ , Site Structure for SEO: https://yoast.com/site-structure-the-ultimate-guide/, and How to Clean Up Your Site Structure: https://yoast.com/how-to-clean-site-structure/
Allow Google to crawl and index important pages within your site. Use Fetch as Googlebot to check that they can be rendered properly. https://kb.yoast.com/kb/fetch-as-googlebot/
Consider using noindex to remove pages you do not want completely from a search. This guide explains more:How Do I Noindex URLs?. https://kb.yoast.com/kb/how-do-i-noindex-urls/
Be sure to then resubmit your sitemap to Google as it will encourage Google to reindex your site and update its index. This guide explains more: Submit Sitemap to Google. https://kb.yoast.com/kb/submit-sitemap-search-engines/#google
You may also wish to contact Google for more information on how they decide which links appear. You may contact Google by making a post on their forums: http://productforums.google.com/forum/?rd=1#!forum/webmaster.
Notice that when using the Yoast SEO plugin, it adds all the necessary Schema that needs to generate the Sitelinks. So, you won’t need to change anything additionally from the plugin.