Finnish population is one of the very rare in the world not carrying mongolian genetics. This can be easily proved through genetical studies. Finland is one of the countries where children of Finnish people do not ever have a mongol spot. However, probably this will increase in the future as now there are many marriages to foreigners in Finland. It is an incorrect claim that Finland is anyhow linked by blood to mongolia.
The roots of this propaganda were in 1960's and earlier when racial studies in Sweden and Germany were common. The link of Finns to Mongolians was created for political reasons based on studies, which were by current standards unscientific.