If you have a separate WordPress website that is already a subdomain, then configuration in cPanel may be slightly different.
Instead of using Alias Domains, you can go to Subdomains and add a second subdomain.
Log in to cPanel, and click Subdomains:
Subdomains option in cPanel
Then, add your second subdomain with the same root as your primary subdomain.
Adding a second subdomain with the same root as primary subdomain
Here is what the final subdomain setup might look like:
Multiple subdomains with the same directory in cPanel