How to create a Multi-Network subsite?

With the multisite install main site and network on s.example.com
you can have the subiste as s.example.com/subsite

you will need to have your multisite as a sub-folder installation and not a sub-domain installation (ref the codex)

As you are using WP-Multi-Network you should be ok to go to create a new site @ s.example.com/wp-admin/network/sites.php. Otherwise if the site has already been created on the Multisite installation go to s.example.com/wp-admin/network/admin.php?page-networks edit the network for s.example.com and select from the available sites the one(s) that you want to add to the s.example.com network.