If I’m understanding your situation correctly, you want to see a list of measurements that include probes from a particular AS as their source. At present, there’s no easy way to make a single API call to get that, but you could synthesise that information by comparing two reasonably small bodies of data.
There are two bulk data downloads that you can use for this: measurement metadata (already mentioned, updated weekly) and the probe data (daily).
Basically, you need to do three things:
asn_v4
          or asn_v6
          equal to the AS in question.probes
          list.Fetch the probe-specific data from the API using both ids:
  https://atlas.ripe.net/api/v1/measurement/**measurement_id**/result/?prb_id=**probe_id**,**probe_id**&format=txt
The above call will
        return all of the results for measurement #${measurement_id},
        but only for probes with one of those two ids. That last bit, format=txt
        will ensure that the returning data is in bite-sized chunks so
        you don’t gobble up 30gb of memory just to parse what comes out.
Write that in a loop with a reasonable wait time between each request or we’ll get mad at you and you’ve got a decent body of data to work with.
Note that there’s no
        reason to fetch the entire history of a measurement either. You
        can always pass start=<timestamp>
        to the above URL and it’ll only give you results returned since
        that date.