Would it be possible for the
Sami people (the Lapplanders) of Northern Scandinavia to form their own nation sometime in the Middle Ages?
Yes, it would be. But nothing with borders like that, and I seriously doubt the long-term survival of it. You'd primarily be looking at the inland areas of Northern Norway/Sweden/Finland. North of the Arctic Circle, and probably less territory in the costal areas.
This area has historically been of fluent/undefined borders, and a lot of wilderness as far as the Scandinavians have been concerned. Before the modern age, the projecting of power here has been difficult, and frankly rather uninteresting and unrewarding. Nomads are a pretty diffuse lot, and as long as Scandinavians got the Lofoten fisheries, theres been very little of economic or strategic interest here. Some fur trade, but nothing you can't get elsewhere.
All of which starts to change around 1800 or so.
Fundamentally, before that you can have a small Saami state as long as you stay away from the Lofoten and south of there coast, because no-one is interested enough to put up the effort to stop you.
Why would the Saami want a state, though? The climate here does not support the agriculture for much in the way of a settled population, pre-potato. I'd go with pressure from some other people leading to some Shaka Zulu-like figure. Or maybe the survival of some remnant of Bjarmland (or Kvænland, but thats probably too far south) slowly diffused into Saami majorities.
To be honest, my suggestion for a POD would be about 500 AD. Have the aggressive intrusion of Saami-speaking people from the east result in a pushback leading to more aggressive cultural traits in the actual Saami people.
(Yes, confusing. The Saami language is actually not the original language of the Saami people, it replaced the original language way back when. And then the new language was named for the Saami people by Europeans, confusing everything.)
The Sami used to enjoy much bigger living areas in Finland and Sweden until the 16th and the 17th centuries, even, before the southern peoples practicing slash-and-burn agriculture moved north and took over those areas. Central and even parts of the southern Finland have a lot of place names derived from the Sami language due to that. And there were very small, isolated Sami communities living in the southern parts of Finland even in the 18th century - pagans, no less.
Eh, there were people still running pagan Norse sacrifices around Egersund till the 1880s.
Anyway, I am told the Saami/Norse settlement issue is even more complex than that. The Saami and Norse have flexed over this area for thousands of years. In periods with warm climate, the Norse agricultural package expands and covers more land. When the climate cools, the Saami nomadic lifestyle outcompetes it somewhat and the Saami expand into areas the Norse have abandoned after one too many crop failiure.