In case of a WordPress multisite with a specific setup trying to run autoupdates, you could add the following to prevent the WordPress autoupdates:
define( 'WP_AUTO_UPDATE_CORE', false );
Hiding the automatic update messages in dashboard for site users and single site admins, you could disable the nag actions:
add_action( 'admin_init', 'dx_prevent_notifications' ); function dx_prevent_notifications() { if ( !current_user_can( 'edit_users' ) ) { remove_action( 'admin_notices', 'maintenance_nag' ); remove_action( 'network_admin_notices', 'maintenance_nag' ); } }