There is TUPAS system, which is kind-of-a-legacy-system used widely in user authentication. It is scheduled for ramp-down but the system replacing it is not yet ready. TUPAS is still de-facto authentication system in Finland.

Telecom operators also provide authentication services (Telia, Elisa, DNA), called Mobiilivarmenne (https://mobiilivarmenne.fi/eng/).

Public sector has suomi.fi authentication. It is (effectively) provided by the government. It is not commercially available.

Both bank IDs & telecom IDs are bundled together by brokers, such as Signicat or Telia. Funny enough, Suomi.fi also offers banks' authentication methods as an option, since only a fraction of the population has a government issued ID card supporting suomi.fi authentication.

The replacement system is an eIDAS-compliant solution, but it is (to my knowledge) still on the drawing board.