The Kven of recent centuries are the Finnish descendants who are in the most northerly reaches of Norway, predominantly in Finnmark.  The old spelling in the Norwegian records included "Qvæn."

The traditional Finnmark area of Norway is called Ruija in Finnish.

In a modern description, just as we talk about ethnic Finns in America as "Finnish Americans," the Kven would be ethnic Finns in Norway or "Finnish Norwegians."

[The ancient "Kven" of "Kvenland" refer to the inhabitants of a broad region that includes some of modern-day northern Finland, northern Sweden, northwestern Russia, and likely even some of northern Norway.]

To confuse matters significantly for researchers today, in the old Norwegian parish records (1800s), those labelled as "qvæn" or "qven" are ethnic Finns and those labelled as "finn" are actually ethnic Saami.  In the 1800s, there were some northern Norwegian communities that actually had more Kven/Finns in them than Norwegians.

Information about the Kven communities:

Wikipedia: Kven people  |  Kven language  |  Origins of the name Kven

Maps of Finnmark region (1861)

Facebook group: Kven Genealogy (created 22 Apr 2017*)

[*inspired to emulate the idea of Mary Lukkarila in creating Finnish Genealogy and Saami Genealogy as wonderful forums]