I am using SharePoint 2013. Within a Task List I want to use the filter A on Top Z on Top. However, it's not changing the titles of the Tasks. Is this something from the Administrator Permission's end or am I doing something wrong?
You are filtering the wrong column. from your image what i am seeing you are filtering the Completed column which has two values ( Yes and No). You are seeing the Only NO because no task is completed yet. If you click on the checkbox on the task then you will see Yes.
Hover the Mouse on the TaskName and then click on dropdown. now you will see all the tasks, Click on the filter which you want
A to z Ascending or
Z to A Descending.