Alaskan Native Americans may be paid in the sense that the government provides subsidies for infrastructure and the like, but it’s seen as either welfare or necessary to allow them to keep practicing some of their native way of life. All Alaskan citizens also get a dividend from the Permanent Fund, but that’s only around $1000 a year. They are definitely not being paid to discourage Russia from invading (except for the military I suppose).

There is an annual payment from the oil money, yes, but it isn't large enough to affect people's decisions about living there, nor is that the intent.