Domain mapping will Not work in a sub-folder.
Not sure if multisite without domain mapping will work in a sub-folder, I'll just say I doubt it.
The domain name you use for WordPress administration has to be going directly to WordPress, no subfolder.
You can install WordPress in the root of your hosting account, or the root of subdomain (created via CPanel or similar). When you set up WordPress in multi-site mode, you pick whether you want "subdomain mode" or "subfolder mode", which is different than where WP is installed.