ahmedimraan

This plugin adds Custom Fields to WP REST API JSON output. Works with Advanced Custom Fields. 
Its as simple as Installing and Activating, once activated you can see an object named metadata.

WP REST API POST/ PAGE CUSTOM FIELDS

Adds Custom Field output to the WP REST API for posts, pages, users, and taxonomies.

Jeremy Pry

Allow Links from the Link Manager to be manipulated and retrieved using the REST API.
This plugin makes the following endpoints available:
<ul>
<li><code>/wp-json/wp/v2/links</code> – List details for all links, or create a new link.</li>
<li><code>/wp-json/wp/v2/links/<id></code> – List details for a particular link ID, update a link, or delete a link.</li>
</ul>
For more information about the REST API as a whole, refer to the <a href="https://wordpress.org/plugins/rest-api/" rel="ugc">REST API plugin</a>.
Note: This plugin requires the <a href="https://wordpress.org/plugins/rest-api/" rel="ugc">REST API plugin</a>.

REST API Link Manager

Enable REST API endpoints for Links in the Link Manager.

WP REST API POST/ PAGE CUSTOM FIELDS vs REST API Link Manager