The Netezza driver only supports username and password authentication: https://onlinehelp.tableau.com/current/pro/desktop/en-us/help.html#examples_netezza.html
Have you tried using the Run As user username and password to connect?
Thanks for the update Carisa. "Run As User" username work if we connect and publish from Tableau Desktop.
My only concern is we are using Service account as Run As User account and due to security reasons the service account should not be shared with individual developers. It should only be used on the server to access databases and file shares.
Have you considered publishing the data source separate from the workbook? You could embed the credentials in the published data source, and users who connected to it to build workbooks would not need to see the credentials:
This a good alternative and this may work without sharing the Run As account username and password. I'll test this option.