Wordpress has a plugin for Permalink Settings through which we can fully customize our URL and structure it into sub-folders as we like.
I want to know if wordpress.com also offers the same feature? Free or paid?
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Permalink settings are not part of hosted blogs on WordPress.com
You can see setting custom post link settings as part of the PHP code behind your blog. (Even if it relies on .htaccess of Apache servers).
If you would like to set your own permalink structure you must host a version of WordPress elsewhere.
Removing this option from the blogs hosted on WordPress.com allows them to better control and maintain the quality of the server and site performances as the wrong type of permalink structure can make a site unusable.