Copy paste the following into your ~/.ssh/config file, modify as appropriate.
ServerAliveInterval is there to help those stuck behind CGNAT, to prevent it from closing the connection if you stay idle too long. You can remove it if not needed.
Telnet command, or local proxy command: “plink %user@%proxyhost -nc %host:%port -pw %pass”
Session -> Default Settings -> Save
Note:
Your private key password is not actually visible within PuTTY, and is still required to access any other terminal session.
However OpenSSH is probably more secure due to this so probably that would be a better option.
This configuration will also apply (in the most part) to some SCP clients, such as WinSCP.
With the exception that for “Local proxy command”, you must use the full path to plink. For example, ‘“C:\Program Files\PuTTY\plink.exe” %user@%proxyhost -nc %host:%port -pw %pass’.