A real-life Cayuga Nation Council member Clint Halftown points out there's a character on the show named Jane Halftown ... who just happens to be a council member. In the suit, Clint calls out a scene where Paul Giamatti's character is discussing a land deal with Jane Halftown that reeks of corruption on the part of the tribe.

According to the suit, the Nation claims "Billions" makes it seem like the Cayuga are all about accepting "unlawful gratuities" and coercing politicians into getting their way.

In the suit, the Nation says "Billions" producers were lazy because they didn't bother to change names -- as in using a fictitious tribe and council member. They claim they DID do that for the main characters. For instance, the show's star, Damian Lewis, plays Bobby Axelrod ... and they claim he's widely considered to be modeled after real-life hedge fund manager Steve Cohen.

Halftown and the Cayuga Nation say Showtime and the show's producers can make things right in two ways: stop referring to the Nation and the Halftown character in future episodes AND compensate the Nation for the damage to its reputation.

Showtime along with producers Brian Koppelman, Andrew Sorkin and David Levien are named as defendants. We've reached out to Showtime, but no word back.