your pics don't show, but I think I know what you mean
take a look at this thread, it should be what your looking for
SG300-10 on 1.3.7.18 Firmware has Double-Login On SSH
https://supportforums.cisco.com/discussion/12296596/sg300-10-13718-firmware-has-double-login-ssh
it refers to this pdf on page 470
http://www.cisco.com/c/dam/en/us/td/docs/switches/lan/csbms/sf30x_sg30x/administration_guide/78-19308-01.pdf
SSH User Authentication
Use the SSH User Authentication page to enable SSH user authentication by
public key and/or password, and (when using authentication by public key) to add
an SSH client user that will be used to create an SSH session in an external SSH
application (like PuTTY).
Before you can add a user, you must generate an RSA or DSA key for the user in
the external SSH key generation/client application (such as PuTTY).
Automatic Login
If you use the SSH User Authentication page to create an SSH username for a user
who is already configured in the local user database. You can prevent additional
authentication by configuring the Automatic Login feature, which works as
follows:
• Enabled—If a user is defined in the local database, and this user passed
SSH Authentication using a public-key, the authentication by the local
database username and password is skipped.
NOTE The configured authentication method for this specific management
method (console, Telnet, SSH and so on) must be Local (i.e. not RADIUS or
TACACS+). See Management Access Method for more details).
• Not Enabled—After successful authentication by SSH public key, even if
the username is configured in the local user database, the user is
authenticated again, as per the configured authentication methods,
configured on the Management Access Authentication page.
