YgoProDeck owns a public endpoint for archetypes, so cards can be associated to them. Note that this is not official and updated by hand. They take feedback for card archetypes here.
The only available endpoint for archetypes is getting them all. This method will return a list of Archetype objects :
$response = $client->archetypes->getAll();This list cannot be filtered.
Archetypes will be sorted A-Z. This is not configurable.