PokéBase - Pokémon Q&A
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YES

it is possible but it is very rare, the chance is 1/8192.Another reason it's possible, Uxie doesn't belong to the illegal Shiny Pokemon.

Unobtainable Shiny Pokémon

In most generations there are a few Pokémon that cannot be obtained Shiny without cheating or glitches, due to either being distribution-exclusive without an in-game location or, in Generation V, being programmed so that they cannot be Shiny in the wild.

Generation II
Mew
Unown forms other than I and V

Generation III
Celebi

Generation IV
Celebi
Spiky-eared Pichu

Generation V
Celebi
Victini
Reshiram
Zekrom
Keldeo
Meloetta
Genesect

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Thanks!
no problem.By the way I edited