Problem in access the list with every one because of Microsoft.SharePoint.Portal.UserProfiles.MySiteLinks.GetMySiteLinks API

Hi All, 

I have a Sharepoint list with EveryOne Contribution permission. The main subsite site did not have EveryOne permission. While I am trying to access the page it's open but with a user prompt, once I drill down I found the authentication problem http://myserver/admin/_api/Microsoft.SharePoint.Portal.UserProfiles.MySiteLinks.GetMySiteLinks

The same scenario is working perfectly with my development environment, Can anyone tell me from where  I can set the permission on this API 

Thanks in Advance