custom_field.php

function api_featured_images( $post ) {
  $field = get_post_meta($post['id'], 'field_id', true);
  return $field;
}

add_action('rest_api_init', function() {
  register_rest_field( 'post, 'field_name', array(
    'get_callback' => 'your_field_function'
  ));
});