If the settings are what is described in the problem description, the user must start an authentication agent on the client side.
Using openssh as client, you should be sure that an agent is running and the environmental variables are properly set:
- SSH_AUTH_SOCK points to a socket where the agent runs
- SSH_AGENT_PID contains the pid of the agent
In case of openssh you also have to load the given key to the agent using the ssh-add command.
If the agent-related environment variables are properly set and the required key is loaded to the agent, then the ssh-add -l command should list you the loaded keys:
$ ssh-add -l
4096 SHA256:1HtkBv514OD//tVbh+kygx/Ll4F4sPlOG6k/jSSycvg pasztor@Pasztors-MacBook-Pro.local (RSA)
When you start openssh client with the ssh command you have to add the -A switch to enable agent forwarding. (Or using the equivalent ForwardAgent in your .ssh/config file relevant to the given target host.)
In this example I assume you installed putty using its installer .msi package.
Using Putty as a client you have to start Pageant first. This is putty's authentication agent.
Then load the desired key into pageant using "Add key".
Configure putty as usual to log in to the target server, but before connect make sure that on the Connection -> SSH -> Auth settings panel the "Allow agent forwarding" option is enabled.