Adding custom ID field to the categories

You can use get_terms():

<?php
$args = array(
    'taxonomy' => 'name-of-the-category',
    'meta_query' => array(
        array(
            'key'       => 'ref',
            'value'     => '53113',
        ),
    ),
);
$terms = get_terms( $args );

You would get an array of terms, where the ref value would be 53113.