When setting up a Map Viewer, using the Add a Web Service tool, You can add Custom Parameters.
The only information I can find on this feature is HERE. Starting at step 4. There is no other reference to what type of queries that will work here.
It is quite frustrating because there is no information on how to set up the Parameter or the Value. It is not the same as just configuring a query in a service's ArcGIS REST Services Directory page. For example, I fell into a discovery that you need a '/' AFTER the layer number (..../rest/services/folder/service_name/0/) when you enter the URL to get the custom parameter to work.
After that, it has been trial and error to figure out what will work here. I have used this to limit the timespan like this:
Value: clock >= CURRENT_TIMESTAMP - INTERVAL '10' MINUTE
Right now, I am trying to figure out how to return features within an envelope that I define.