I'm really not sure that's possible with the Mediawiki API. It was not possible a few years ago and I don't think the feature has been implemented since then.
But Open Refine has a reconciliation service with Wikidata based on an API that can filter by type ("instance of") or property. Its developer has not yet advertised it explicitly as a standalone API, but this is in project. Here is an example of use: find in Wikidata the people called "arturo" instances of human (Q5) and whose occupation (P106) is actor (Q33999).
https://tools.wmflabs.org/openrefine-wikidata/en/api?query={
"query":"arturo",
"limit":6,
"type" : "Q5",
"properties" : [
{ "pid" : "P106" , "v" : "Q33999"}
]
}
Result.
The main problem with this query is it will only return Arturos which are explicitly an instance of Q5. This will be the case of this one, but not of those who are, for example, only instance of "film maker" (and it does not matter that film maker is himself a subclass of "human"). Sparql can handle class transitivity using the property paths (eg : wdt:P279*/wdt:P31*), but this API has not (yet) implemented them.