When a WebSocket server requires secure connections, you can get an error message like this when a client tries to connect to server:

This error means that your client is trying to connect using a TLS version which is not supported by server. To resolver this error you must handle OnSSLAfterCreateHandler of websocket client component and set a newer TLS version. For example: here we are setting TLS 1.2 as protocol version.

procedure OnSSLAfterCreateHandler(Sender: TObject; aType: TwsSSLHandler; aSSLHandler: TIdSSLIOHandlerSocketBase);
begin
   TIdServerIOHandlerSSLOpenSSL(aSSLHandler).SSLOptions.Method:= sslvTLSv1_2;
end;