Creating Subdomain without cpanel

Hi, I would like to know if I can create a Subdomain without the use of cpanel.

I am using my own webhost server without cpanel and registered my domain from namecheap.com

From namecheap website, I have access to DNS and hostname settings.

So what I tried was direct subdomain.domain.com to domain.com/subdomain.
For Record Type, there are 3 I can use for this purpose, URL Redirect, URL Redirect(301) and URL Frame.

URL Redirect just directs traffic to domain.com/subdomain. URL Frame masks/hides the targetted url. But that doesn’t seem right as it only creates a frame above the actual url.

The subdomain should be like food.about.com, where when I navigate, I can see food.about.com/spicy and not about.com/food/spicy.
SEMrush

My purpose of creating a subdomain is to place different content on it and have search engines treat it as (almost) a separate site as my domain site.

Any anyone tell me how I should create my subdomain correctly without the use of cpanel?

Thanks in advance :)