Serpentfolk are a somewhat obscure idea that seems to base itself on the idea "lizardfolk are kind of cool, but how can we make them cooler and/or more evil? Hmm... let's base 'em on snakes!" and working from there.
Serpentfolk, known at the time as Serpentmen or Snakemen, first appeared in the works of Robert E. Howard as part of his King Kull stories, more obscure "predecessors" to those of Conan the Barbarian. Serpentfolk were depicted as a pre-human sapient species of black magicians that had dominated the world, until Atlantis had arisen and defeated them. They also were slowly and tentatively assimilated into first the Conan stories and then, through Howard's correspondence with H.P. Lovecraft, into the Cthulhu Mythos. This is something cemented by the fact that Lovecraft (alongside Zealia Bishop) created a patron deity for the Serpentfolk in the form of Yig, Father of Serpents, in the story "The Curse of Yig".
As such, Cthulhan Serpentfolk have repeatedly appeared in the various editions of Call of Cthulhu.
Over in Dungeons & Dragons, although serpentfolk haven't directly appeared, the Yuan-ti, a species of human/snake hybrids who are divided into castes based on how great the ratio of human to snake is, with the more serpentine being more respected, and with a propensity towards all kinds of fucked up mutations, are pretty obviously made in the Serpentfolk mold. They play a big role in the backstory of the Forgotten Realms, though they cannot seem to keep a patron deity for more than an edition or two, as seen with the long and messed up history of Merrshaulk. The Yuan-ti of Forgotten Realms were created by an older race of snake people called the Sarrukh, who do not exist in other settings. The other major serpentfolk race in D&D is the naga. Another famous one is the Marilith, a type of demon.
Pathfinder, meanwhile, being unable to use Yuan-Ti, simply said "fuck it" and used the public domain Serpentfolk outright. They also feature the naga, and bring back the snake-bodied lamia olf Advanced Dungeons & Dragons as the Lamia Matriarchs.
In Fighting Fantasy there are Serpentfolk called the Caarth who live beyond the a Desert of Skulls. They aren't keen on the Lizardfolk, but both are evil.