What is the correct way to search 3 custom fields only in WordPress?

Are you using Advanced Custom Fields?(ACF?).

Relevanssi is a really good plugin which increases the scope of the core WordPress search.

Here’s the link: https://wordpress.org/plugins/relevanssi/

It allows users to search for posts via ACF fields attached to them.

Once you install the plugin, you can use the following code in your functions.php file to instruct your search to show posts which match meta values.

function rlv_relationship_content( $content, $post ) {
    // Fetching the post data by the relationship field.
    $relationships = get_post_meta( $post->ID, '_cth_featured_zip_code_1', true );

    if ( ! is_array( $relationships ) ) {
        $relationships = array( $relationships );
    }

    foreach ( $relationships as $related_post ) {
        $content .= ' ' . get_the_title( $related_post );
    }

    return $content;
}
add_filter( 'relevanssi_content_to_index', 'rlv_relationship_content', 10, 2 );