Disable update notification for individual plugins / All

code for the plugin file itself:-

// remove update notice for forked plugins
function remove_update_notifications($value) {

    if ( isset( $value ) && is_object( $value ) ) {
        unset( $value->response[ plugin_basename(__FILE__) ] );
    }

    return $value;
}
add_filter( 'site_transient_update_plugins', 'remove_update_notifications' );

I like to put this in the actual plugin. Since I’ve only ever disabled updates on a plugin because I’ve edited or forked the code and don’t want to lose my edits on an update, I’ve already edited the plugin and thus don’t mind editing it more. It keeps my functions file a bit cleaner. But if you wish you can put it in the functions file and a benefit to that method is you can remove multiple plugins from updates by adding another unset line for that plugin like so (code for functions.php):

// remove update notice for forked plugins
function remove_update_notifications( $value ) {

    if ( isset( $value ) && is_object( $value ) ) {
        unset( $value->response[ 'hello.php' ] );
        unset( $value->response[ 'akismet/akismet.php' ] );
    }

    return $value;
}
add_filter( 'site_transient_update_plugins', 'remove_update_notifications' );

Disable All Update Notifications with Code

function remove_core_updates(){
 global $wp_version;return(object) array('last_checked'=> time(),'version_checked'=> $wp_version,);
}
add_filter('pre_site_transient_update_core','remove_core_updates');
add_filter('pre_site_transient_update_plugins','remove_core_updates');
add_filter('pre_site_transient_update_themes','remove_core_updates');