How to add a new plugin page under desired Options page?

Use add_submenu_page instead.

 <?php add_submenu_page( $parent_slug, $page_title, $menu_title, $capability, $menu_slug, $function ); ?> 

$parent_slug should be one of the following

For Dashboard: add_submenu_page( 'index.php', ... ); Also see add_dashboard_page()
For Posts: add_submenu_page( 'edit.php', ... ); Also see Also see add_posts_page()
For Media: add_submenu_page( 'upload.php', ... ); Also see add_media_page()
For Links: add_submenu_page( 'link-manager.php', ... ); Also see add_links_page()
For Pages: add_submenu_page( 'edit.php?post_type=page', ... ); Also see add_pages_page()
For Comments: add_submenu_page( 'edit-comments.php', ... ); Also see add_comments_page()
For Custom Post Types: add_submenu_page( 'edit.php?post_type=your_post_type', ... );
For Appearance: add_submenu_page( 'themes.php', ... ); Also see add_theme_page()
For Plugins: add_submenu_page( 'plugins.php', ... ); Also see add_plugins_page()
For Users: add_submenu_page( 'users.php', ... ); Also see add_users_page()
For Tools: add_submenu_page( 'tools.php', ... ); Also see add_management_page()
For Settings: add_submenu_page( 'options-general.php', ... ); Also see add_options_page()

Example:

add_submenu_page( 'tools.php', 'My Custom Submenu Page', 'My Custom Submenu Page', 'manage_options', 'my-custom-submenu-page', 'my_custom_submenu_page_callback' );