(or Kitty to be more exact, which is Putty on steroids)
1. Set up key authentication to your host with PuttyGen & Pageant (ssh-agent for Putty) – or KittyGen & Kageant if you’re using Kitty. Paste your public key into authorized_hosts on the gateway & destination box.
2. Set up your configuration, IP address in session should be of destination (see screenshot, this is an internal IP).
3. Go to Connection -> SSH -> Auth. Check Allow agent forwarding.
4. Connection -> Proxy. Enter your gateway IP in Proxy hostname & exclude Hosts, choose Proxy type local & put your username in the box.
In telnet command put
klink.exe %user@%proxyhost -nc %host:%port \n
(or plink.exe if using putty). This will be run first to tunnel your connection through.
5. Done!