Disable email notification from WordPress core updates on your child site.
Snippet Type
Execute on wp-config.php on Child Sites
Snippet
add_filter( 'auto_core_update_send_email', 'wpb_stop_auto_update_emails', 10, 4 );
function wpb_stop_update_emails( $send, $type, $core_update, $result ) {
if ( ! empty( $type ) && $type == 'success' ) {
return false;
}
return true;
}