What you asking is almost the same as this.
If you don't want to copy key from gateway to local box, the work around is use Method 1 (bash alias) in that post(and below). ssh_config cannot do what you want. I have detail explanation there about the difference between alias and tunnel method, which include ssh_config
~/.bashrc, add following line
alias ssh-test='ssh -t gateway ssh test@test'
In command prompt, just type following
ssh -t gateway ssh test@test do is almost the same as follow
local# ssh gateway
gateway# ssh test@test
Other than combining the two step in one, it skip opening a shell(csh, bash, etc) on
gateway, instead starting a ssh session to
test right after authentication.
You don't need ~/.ssh/config on local box BUT keep the one gateway for the
test (for key usage).
ForwardAgent yes to gatway
If you don't want to copy gateway key to local box, but permitted to install your
local ssh key into
test@test. Then you can use following
User <gateway user>
ProxyCommand ssh gateway nc %h %p