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Barry is a Pokemon Trainer from Sinnoh. He was shown to have a very hyperactive personality. When he ran into Ash, he demanded Ash pay a large amount of money as compensation for crashing into him within 10 seconds, and he even counted down the time on his Pokétch, and after 4 seconds, seeing as how Ash was still staring at him completely bewildered, Barry started complaining "as if I have time to do this!".

Barry admires Paul and his training methods, and wants to be a strong Trainer like him. He also has a slightly similar mentality as Paul's, as in capturing strong Pokémon for training. However, unlike Paul, he still cares for his Pokémon.

Dawn knew Barry back when they both lived in Twinleaf Town, however, Barry doesn't remember her. He only recognizes Ash, Brock, and Dawn due to the fact that they participated in the Sinnoh Double Battle Tournament with Paul.
It was also revealed that he was good friends with Dawn's rival, Kenny.

(Source: Bulbapedia, edited)