Setting up a minecraft server on a website

Solution 1:

No, there is no way as far as I'm concerned. I'm pretty sure you mite have to invest in a dedicated server (with lots of RAM) as there is generally no way of executing the server through your host.

Or you could just host the server on your own PC

Solution 2:

No. Your web host will likely be what's called "shared hosting". This means the hoster runs a large number on websites on the same host. You'd be able to upload the server .exe or .jar to your server but you couldn't run it. You'd need to run it on your PC or use a proper minecraft server host.

Solution 3:

Your website is located on a web hosting. This means that that machine runs only one program (well, a set of programs) you have access to - a web server, that serves pages for browsers. To set up a Minecraft world, you will need to run a completely different program - a Minecraft server. This requires you to have operating-system-level access to the server, which cheap web hosters do not provide.

You will need either a private server with full access (expensive) or rent a Minecraft server from some specialized service (there are some, just like with web servers).

On the bright side, you'll probably be able to bind that rented Minecraft server to the same domain name, like mc.asifslab.com, though it will be physically in another place.