The URI for that endpoint would look something like this;
https://api2.frontapp.com/conversations?qqstatuses]=assigned
However, I would suggest you explore the conversation search endpoint, which offers more search options, and provides a helpful _total field in the result letting you know how many results matched your query. We also provide a Search tutorial for the conversation search endpoint.
Something like the following might be more appropriate as it allows us to filter for conversations which are both assigned and open (rather than everything assigned, regardless of it's open/archived status):
https://api2.frontapp.com/conversations/search/is:assigned%20is:open
--Jason