Host part of a website at home???

Question

Hello,

I am planning to setup Nextcloud on my old computer and I want to connect it to my website however use it as something like: "cloud.mywebsite.com" or "www.mywebsite.com/cloud". My website is not going to be hosted at home however I want to somehow host this bit of the website at home (so I could maintain it myself). Is there any way to do this or something like this?