Yes, Product Slider Pro for Woocommerce is fully compatible with the Yith Woocommerce Badge Management plugin. You need to paste the following code into your current theme’s functions.php file:

For Yith Woocommerce Badge Management free.

if (defined( 'YITH_WCBM_FREE_INIT' ) && YITH_WCBM_FREE_INIT && function_exists('YITH_WCBM_Frontend')){ 
add_filter( 'sp_wpspro_product_image', array( YITH_WCBM_Frontend(), 'show_badge_on_product_thumbnail' ), 99, 2 ); 
}

For Yith Woocommerce Badge Management premium.

if (defined( 'YITH_WCBM_PREMIUM' ) && YITH_WCBM_PREMIUM && function_exists('YITH_WCBM_Frontend')){ 
add_filter( 'sp_wpspro_product_image', array( YITH_WCBM_Frontend(), 'show_badge_on_product_thumbnail' ), 99, 2 ); 
}