It is the connection as sysdba, not sysdba at SID.
Conn un/pwd@sid as sysdba, not conn un/pwd as sysdba @sid.
You will have to use the password since you are not on the server. You won't get the benefit of OS authentication.
If you are on the server, you can do things like conn fake_un/fake_pwd as sysdba and still connect. If over the network, you have to use real username and password.
Can you use/try conn username@sid as sysdba and get a prompt for the password?