Thanks for reaching out to us on PI Square. Likely what the error you're receiving is, is that you don't have a Kerberos ticket which allows you to ask for data from the Web API service. I'm not a java programmer myself, but perhaps if you shared a snippet of your code we could take a look at how the HTTP client is being set up and the request is being made to see if there's any changes necessary to allow for Kerberos authentication in the code. I know Oracle has some documentation on setting up clients to authenticate with Kerberos we could reference against.
I think it's also worth making sure that your user is able to connect and authenticate using Kerberos. On the machine where you're testing this java app, could you please navigate to the system/userinfo endpoint for the pi web api and confirm that the account that's running the java application is able to be impersonated. You should see something like the following:
vs in the below where you see the service account running the pi web api's credentials and Impersonation Level is "None"