Authorization Required on public Site

The "authentication required" error happens when the site user experiences an error, such as not having permission to a field, a null-pointer exception, etc.

1. Try using the debug logs for the sites user. Setup > Monitoring > Debug Logs, enable the sites user, generate the error, and check the logs.
2. Turn on development mode for your admin user (Setup > Personal Information) and try viewing the page. You might be able to see the error directly (assuming this is a code problem and not a security issue).
3. Setup an alternate Visualforce page to capture the error from the first page, and return the errors back to that page.

More details can be found here: Debugging Sites Authorization Required Error.

Two steps:

1. First go to Setup write VisualForce pages" and reach to VF page list. Here you will find the page you need to access.

   • Click on Preview for Webpage. The web page will open in separate window. Access this from your profile and not from guest user. There you can see errors with specific name of the object. For example if it is not able to access an object. It will mention the name of object that is seeking permissions.

2. Go to Setup

   • type Domain in quick find.
   • Click on "Custom URLs"
   • Next you will find sites details click on Site label. It will lead to all details for site.
   • Click on button Public Access Settings that will open profile access page.
   • Click on App section
   • Click on Object Settings (we are assuming we have an object access problem, which is most often the case.)
   • That will open all Objects page, now you have select object accessed by visual force page in question or object identified in first step.
   • So it now simply Profile Overview  Object Settings  Selected object name (let's say Accounts)
   • Click on Edit and give read and write access
   • Click save.

Now try your app again. I hope then Authorization problem gets resolved.

You can not have access to Account from a public site when you use standard controller, only if the guest user has created the account which is not the case for you. That's Salesforce standard security. You will have probably to create a custom controller set as 'public without sharing' or 'global'.