connecting to a sftp site with a public key

one of my client sent me a public key to connect to his SFTP site. If any one can help he how to transfer the files to SFTP using public key.

You specify your private key here:
https://winscp.net/eng/docs/ui_login_authentication

I assume that it's a private key. You cannot connect with a public key. Unless it's a host public key.
If that's the case, see https://winscp.net/eng/docs/ssh_verifying_the_host_key