You have to fly to Sandgem town and go to Lucas's/Dawn's house and talk to the little girl who's addicted to TV. She may say that the TV is talking about Skitty swarming on Route 222 which is west of Sunyshore and you will need to go there to encounter Skitty. (She may not say it's Skitty that day.)
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No, but skitty can be caught on route 222 in Pokemon diamond pearl and platinum
swarms on route 222
You cannot find skitty in-game. Tansfer it from another generation
On Pokemon Sapphire, you can find a skitty on route 116, near the Rusturf Tunnel, but it's very hard to find. You have about a 2% chance of finding one!
Skitty can be found on route 116 However, it is very hard to find but trust me its there!