Q:

GetListItems Using system Account in SPServices SP2013

How can I use GetListItems Using system Account in SPServices SP2013

A:

It is not possible to pass the system account username and password as parameter in any client side programming like SPServices. It will always use your client credential(through browser). 
Suppose it is possible to use system account credential in the client side programming, then that password can be accessed from any browser which I think is not a recommended way as system account password is has permission to delete that list or the whole web application. So a person having knowledge in SpService easily can delete that list using browser console, I think which is a major security threat for any web application.
If that list has view permission for all(NT-Authority), GetListItems will automatically work using the user's permission.

