Concepts don’t belong to a concept source really, I think what you want is to fetch concepts that have mappings to a given concept source and to get them you only specify the source parameter, its value can be a concept source uuid or name.
Searching for concepts with mappings to a given source by a partial code isn’t supported even in the core concept API and doesn’t support searching by name anyways, you would have to add a custom search handler that first performs the regular partial search by name and then manually filter out concepts that don’t have mappings to the specified source.
Alternatively you need to build your UI in a smarter way, the user should first select a concept source, and then the name search follows which you perform against the returned concepts on the client side.