Fairy does ×1 to Psychic

Generations VI to IX, single types. The other way round, Psychic against Fairy, is ×1.

64 Fairy and 102 Psychic species among the 1025 this site covers.

Attacker, Psychic and Fairy Hatterene sprite

damage×1Generations VI to IX

Defender, Psychic and Flying Lugia sprite

Lugia #0249

Fairy did not exist in Generation I and Generations II to V, so Fairy against Psychic has no value there.

Strongest Fairy attackers

Hatterene leads Fairy at Sp. Atk 136

Sturdiest Psychic defenders

Dual types that change the answer