Sorry again for this basic questions but i see that many developers have not clear ideas

This is my subdomain: subdomain.example.com that want to use for a very simple rail app.
This is my .conf file:

# domain: subdomain.example.com
# public: /var/www/subdomain.example.com/public_html/

<VirtualHost *:80>
  # Admin email, Server Name (domain name), and any aliases
  ServerAdmin webmaster@example.com
  ServerName  www.subdomain.example.com
  ServerAlias subdomain.example.com

  # Index file and Document Root (where the public files are located)
  DirectoryIndex index.html index.php
  DocumentRoot /var/www/subdomain.example.com/public_html
  
  <Directory /var/www/subdomain.example.com/public_html>

  # Log file locations
  LogLevel warn
  ErrorLog  /var/www/subdomain.example.com/log/error.log
  CustomLog /var/www/subdomain.example.com/log/access.log combined
</VirtualHost>

The question is: the ServerAlias must be "subdomain.example.com" OR "example.com"?
And please confirm, this setting is independent if i manage my domains DNS from "Linode DNS Manager" OR from my "Registrar DNS Panel"?

so why you use "www.subdomain.example.com" ?
if you want to create subdomain it's better just create subdomain.example.com, it think if you use www.subdomain.example.com it's subdomain in subdomain.
serveralias is just optional you just need ServerName subdomain.example.com if you want to create subdomain.example.com

so the conf is:
<VirtualHost *:80>
# Admin email, Server Name (domain name), and any aliases
ServerAdmin webmaster@example.com
ServerName subdomain.example.com

# Index file and Document Root (where the public files are located)
DirectoryIndex index.html index.php
DocumentRoot /var/www/subdomain.example.com/public_html

<Directory /var/www/subdomain.example.com/public_html>

# Log file locations
LogLevel warn
ErrorLog /var/www/subdomain.example.com/log/error.log
CustomLog /var/www/subdomain.example.com/log/access.log combined
</VirtualHost>

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APKTrunk - Android APK Collection

That's actually how I would do it.