api request with filtering by custom field for Wordpress REST API v1 see: https://github.com/WP-API/WP-API/issues/1060

function.php

add_filter( 'json_query_vars', 'slug_allow_meta' );
function slug_allow_meta( $valid_vars ) {
  $valid_vars = array_merge( $valid_vars, array( 'meta_key', 'meta_value' ) );
  return $valid_vars;
}

sample.js

$.ajax({
  type: 'GET',
  url: 'http://xxxxxxxxxx/wp-json/posts?filter[posts_per_page]=20&type[]=page&filter[orderby]=rand&filter[meta_key]=XXXXX&filter[meta_value]=YYYYY',
  dataType: 'json'
}).done(function(json){
  console.log(json);
}).fail(function(json){
});