i think you’re talking about the results that show up in the “Species” section of the “Explore” page. if that’s what you’re talking about, there’s not a way to directly order that list.
however, you could get the underlying data for that list via the API, and then you could order the data however you like. here’s an example of the page that shows the kind of data that’s available from the API: https://jumear.github.io/stirfry/iNatAPIv1_observations_species_counts.html?place_id=7887&options=ancestry.
if you’re trying to get a species list for a place, you could also accomplish something like that via the place checklists, though those may reflect additional species not recorded as observations in iNat. see: https://forum.inaturalist.org/t/simplified-species-list/25967/6.
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if you’re actually talking about sorting records in the “Observations” section of the “Explore” page, the best you can do there (short of downloading the observations and then sorting yourself) is to apply a &order_by=species_guess parameter to your URL. the problem with this approach is that species_guess can be unpredictable. it might reflect common name, common name in some other language, or scientific name (if no common name).