I generate sitemap and it says "Your sitemap file was created in the root directory of the site. Options saved." However, checking the root of my site, shows it is not actually there.

Please make sure that you are checking the WordPress root (WordPress can be placed not in the root, but in the subfolder. In this case, you should search the sitemap in the subfolder).

Also, make sure that none of your PHP security directives for that domain is disabling file-write.

This article related to Sitemap by BestWebSoft plugin

Additional resources: Sitemap - User Guide

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