I have a website asifslab.com and I want to set up a minecraft server there so that it is 24/7. Is there any way to do this through FTP or cPanel or will I have to set it up on my PC?
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.