Pokemon Gold, Silver and Crystal introduced the concept of Shiny Pokemon, and in order to retain shininess of a Pokemon that was traded to Pokemon Red, Blue, Yellow, Green,
Shininess was set to be determined by a Pokemon's Determinant Values (DVs).
As such, this mechanic also allowed for Pokemon caught or received in Gen I with the correct DV combination to become shiny when traded to Gen II.
Additionally, with the introduction of Generation I & II to the Virtual Console on the Nintendo 3DS, these shiny Pokemon can be transported up to Generation VII and remain shiny.
Generation I's RNG - DV correlation has been analyzed, and it has been discovered that only certain Pokemon can be encountered legitimately shiny (ignoring using glitches),
mainly: (1) received by in-game trade, (2) encountered by fishing, (3) stationary encounters, (4) gift (starters, Eevee, game corner, etc).
Do note that confusion may arise, if a shiny Pokemon was hatched/caught in Gen II, and traded back to Gen I, before transported to Gen VII.
(Even if hatched/caught in Gen II, it will say from Kanto if it was transferred from Gen I)
The google sheet below shows the list of Pokemon relating to Gen I shiny legality, and other pages involving RNG-DV correlation based on encounter rate.