Custom fields for custom post type

You need to add your own metabox for the custom post type created. You can use the action add_meta_boxes_{cpt_slug}

add_action( 'add_meta_boxes_' . $cpt_public_slug, 'adding_custom_meta_boxes' );
add_action( 'save_post', 'save_metabox' , 10, 2 );

function adding_custom_meta_boxes(){
    global $cpt_public_slug;
    add_meta_box(
        'plugin-site',
        __( 'Website', 'text_domain' ),
        'cpt_form_site_Render',
        $cpt_public_slug,
        'normal',
        'high'
    );
}

function cpt_form_site_Render(){
    global $post;

    $post_meta = get_post_meta($post->ID); 

    // render the input field
    ?>
     <input type="text" name="meta_key" value="<?php echo $post_meta['meta_value'][0]; ?>"/>
    <?php
    // do it for all your metas
}

function save_metabox($post_id, $post){

    foreach ($_POST as $the_posted_key=>$the_posted_value) {
        if (strpos($the_posted_key, brozzme_passport_config::$custom_fields_prefix)!==false) {
            update_post_meta($post_id, $the_posted_key, $the_posted_value);
        }
    }
}