How does Edmund represent Judas in The Chronicles of Narnia?

Edmund betrayed Aslan and his siblings, just like Judas Iscariot betrayed Jesus and the Apostles.

The "Turkish Delight" represents the silver that Judas betrayed Jesus for and The White Witch represents Satan.

The Pevensie siblings represent the Apostles:

Peter - Saint Peter. He loses his faith later, but finds it again, just like Saint Peter did. He is reckless and brash just like Saint Peter was.

Lucy - Saint John. John believed the most in Jesus, just like Lucy believes the most in Aslan.

Susan- Saint Thomas, "Doubting Thomas". Susan doubted the most, ever since the beginning. She also loses her faith in Narnia completely, that's why she never reaches Narnia ("Aslan's Country", which is a synonym for Heaven) along with her siblings, ever again.