No, you can't find shiny Pawmi in Pokemon Go
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Pawmi, mouse Pokémon from Paldea, is found in the wild in Pokémon Go. No, Pawmi can't be shiny in Pokemon Go!
Paldea's electric mouse Pokemon is simply too new to the game. Pawmi's shiny will likely be added in a future update or event, most likely one to do with Paldea, walks, or electric types. Phooey.
According to old research from the now-defunct website The Silph Road (via the Wayback Machine), the shiny speed of Pokemon on a typical day is about one in 500. Pawmi is not a confirmed Pokemon that gets a "permaboost" (meaning it's a rare spawn and thus gain a boosted shine rate).