For your reverse proxy, you do want to have a domain and point it to the IP of your VPS with an A record. This is done in the DNS section of your domain provider. Basically, publish a DNS record that says jellyfin.yourdomain.com has as a target the public IP.

Use apache2 as a reverse proxy. You basically need to copy the files in the Jellyfin documentation. But start by just creating a reverse proxy file, which you can use to get the Let Encrypt certificate for your domain.

Enable the site this file first:

ServerName jellyfin.yourdomain.com ProxyPreserveHost On ProxyPass /.well-known ! ProxyPass / http://localhost:8096/ ProxyPassReverse / http://localhost:8096/

Try to reach it from the browser using the subdomain. Let me know if you need more help after that.