This constructor is deprecated because it is no longer necessary to explicitly indicate the access type, as the API can infer this from your app key:
AndroidAuthSession(AppKeyPair appKeyPair, Session.AccessType type, AccessTokenPair accessTokenPair)
Instead, you can use this constructor:
AndroidAuthSession(AppKeyPair appKeyPair, AccessTokenPair accessTokenPair)
Note, in the current version of the SDK, this version is also marked deprecated, but this is mistaken and will be corrected in the future.
In any case, using a deprecated constructor like this shouldn't actually cause an error, so it sounds like you may want to ask another question with the details of the error you are getting.