Despite encountering mythical Pokémon and Pokémon from other worlds, the rarest Pokémon Ash ever had was caught long, long ago.
Ash of Pokémon has encountered many rare Pokémon during his journey, from Pokémon gods to alien Pokémon from other universes. Of course, he catches far fewer, but one of the rarest Pokémon Ash has is also one of his oldest.
Despite the show's motto "Catch them all!", Ash respects legendary and mythical Pokémon, which are often shown to be able to talk in the anime, and rarely attempts to capture them. The only exception is Meltan, although it is a myth, it is only one of them. Many would say that Meltan's evolution, Melmetal, is the absolute rarest Pokémon he's captured and fought since it's still a Mythic Pokémon, and that's a fair point. Even his Poipole (which he had for a relatively short time) is pretty rare since it's from another world, but Poipoles are said to be starter Pokémon in the in-game world, suggesting they're relatively easy to obtain in their home world. Instead, the rarest Pokémon Ash caught was a Pokémon that could be traced back to Johto: Night Owl.
In "Fowl Play!" Ash meets a very rare Pokémon, a shiny owl. Shiny Pokémon are Pokémon with rare mutations that make them look different from other species; this difference can be very noticeable (many Shiny ones are pink) or barely noticeable (Some Shiny ones are just changed their eye color). The Noctowl is more striking, and when Ash sees it, he discovers that another is already trying to capture it. As it turns out, the Noctowl is very smart and consistently outsmarts the person trying to catch it, so he decides to give Ash a try. Ash uses Pikachu, who is hypnotized by Night Owl's hypnotism and randomly fires lightning before finally getting rid of it. Pikachu escapes the hypnosis by closing his eyes and listening to Night Owl's wings, attacking the source of the sound and defeating Night Owl, allowing Ash to catch it.
Shiny Pokémon in the Anime Are Even Rarer Than Legendaries
Shiny Pokémon are extremely rare, around 1:8,000 at the time, so they don't appear very often in the anime. Shinies are a new mechanic in the Johto-based Gold and Silver game, so it made sense to include that new feature in the anime as well, and highlight this by making it Ash's Pokémon Sure to get the kids excited. Ash's Noctowl is also unique for its size, as it is much smaller than other Noctowls in the area. The latest games, Scarlet and Violet, include size-changing features, and getting very small Pokémon is extremely difficult, so little shiny Pokémon like Ash's Noctowl are actually even rarer than regular shiny ones. Ash still has his owl and keeps it in Professor Oak's lab along with most of the other Pokémon. The fact that it's shiny is rarely noticed these days, so many new fans may not even know that Ash has had a shiny Pokémon all along!
With Ash returning for one final miniseries before his character's retirement from the Pokémon anime, fans can only hope that Ash's shiny night owl will play the character one last time before it wraps up.