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.

Kite

Due to security/privacy concerns, JSON REST API (WP API) only allows post meta data (custom field value) for authenticated users. 
This plugin is an easy way to make post meta available when unauthenticated.
After activate the plugin, go to WP API Customizer option page. 
Click the plus icon to add rows. 
Set JSON attributes and custom field names in your posts that you want to use when unauthenticated. 
The JSON REST API will provide the data as “post_meta” like the following:
<pre><code>"post_meta":{"your_attribute_a":"Custom Field A value","your_attribute_b":"Custom Field B value"}
</code></pre>

WP API Customizer

Make post meta data (custom field values) available for JSON REST API (WP API) when unauthenticated.

WP REST API POST/ PAGE CUSTOM FIELDS vs WP API Customizer