My question is that is there anywhere in the books that a girl with brown skin is better than a girl with fair skin or while choosing girl for marriage brown skin girl is better compares to fair skin girl?

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I am not aware of anything like that.

The Messenger of Allah (S) has forewarned, “A man who marries a woman for the sake of her wealth, Allah leaves him in his own condition, and one who marries her (only) for her beauty, will find in her (things) which he dislikes (unpleasing manners) and Allah will gather up all these things for one who marries her for the sake of her faith (religiousness).”