Mutant, by Henry Kuttner - a collection of SF stories set in a common background: these are the "Baldy" stories, with some connecting material. Henry Kuttner is one of the most able and versatile writers of short fiction. In my opinion, these have lasting power and are still readable even after 50 years, unlike much early SF.

The Big Blow-up left huge radioactive sores (the graves of cities) all over the planet. In time, from some of the women who had been near these shunned areas, the first totally hairless babies began to be born. At first, no differences were noted. But eventually they became known as "Baldies" - and new and terrifying difference became apparent. The Baldies were telepathic. From then on they were hated by normal humans - and hunted like animals. This is the story of their struggle for survival and their desperate search to find a safe means of giving the power of telepathy to humans so that both kinds might live peacefully side by side.

(Framing narrative: One, Two, Three, Four, Five, Six)
The Piper's Son
Three Blind Mice
The Lion and the Unicorn
Beggars in Velvet
Humpty Dumpty

All stories first appeared in Astounding as by "Lewis Padgett" - the first 4 in 1945, the last in 1953. The first book version (also as by "Lewis Padgett") was a hardcover in 1953 from Gnome Press - the framing pieces are original to that. As is typical for most collections or fix-ups with a framing narrative, I recommend the stories as much better than the "pudding" they're embedded in.