Add a Custom Permalink option in the Permalink Admin Screen?

To hook your custom plugin settings into the Permalink settings, use the following:

add_action('admin_init', 'wpse_237141_custom_permalink_section');

function wpse_237141_custom_permalink_section() {
    add_settings_section(
        'your_custom_id', // ID
        'Your Plugin Settings', // Section title
        'your_callback', // Callback for your function
        'permalink' // Location (Settings > Permalinks)
    );
}

You’ll need to fill in the blanks to display your own custom functions, but this will now display your settings in the Permalinks.