I think that this was a rather old novel, some children developing telepathic skills on different parts of the world, getting in contact with each other, maybe some disabled telepath, and then them gathering together on an isle in order to establish their own evolved society. If I remember right, people are sending marine ships to the isle in order to blow them to kingdom come...
You have described the last half of the 1935 novel Odd John by Olaf Stapledon. (The term "homo superior" comes from this book.) Maybe one of these covers will be familiar. The full text is available at Project Gutenberg Australia. The following chapter-by-chapter outline is from the Wikipedia page (emphasis added):
- John and Author. A physical description of John Wainwright.
- The First Phase. His parents, and his life from birth (around 1910) to five years of age. At the age of four, he learns to speak; nine months later, he learns to count. He claims to learn all of mathematics, and develops an ability to visualise n-dimensional space.
- Enfant Terrible. He learns to walk at the age of six, and practises acrobatics and fighting with a neighbourhood boy called Stephen. He studies biology and jujitsu.
- John and his Elders. John's relationships with people around him. He is taken to see factories and mines, and waylays people of interest to interview them. The interview with "Mr Magnate".
- Thought and Action. John occupies himself with toys, and studies philosophy. His burglaries, and his murder of Smithson.
- Many Inventions. John's friendship with the six-year-old Judy. His secret laboratory and his inventions.
- Financial Ventures. John uses the author as a go-between to sell the inventions. He speculates financially and is cheated. He tries to study directly with financiers.
- Scandalous Adolescence. John has gay affairs, and courts a much older woman named Europa. After that, it is indirectly hinted that he copulated with his own mother.
- Methods of a Young Anthropologist. John interviews famous people using various ruses. He travels to France, Germany, Italy and Scandinavia. He plays the part of a backward child while visiting a psychiatrist.
- The World's Plight. John discusses current affairs with the narrator, and asserts that he has no interest in helping humanity.
- Strange Encounters. John goes on "holiday" in Scotland, and the narrator hears bizarre reports from two climbers named McWhist and Norton.
- John in the Wilderness. John returns and gives an account of his austerities and his spiritual experiences.
- John Seeks his Kind. He develops telepathy, and uses it to discover two beings similar to himself: a musical madman named James Jones, and a crippled child in the Hebrides.
- Engineering Problems. He conceives the idea of creating a colony of "supernormals", and builds a yacht and a plane.
- Jacqueline. The story of a superhuman in Paris, who was born in 1765.
- Adlan. The story of a superhuman in Egypt, born in 1512, who communicates with John 35 years after his own death.
- Ng-Gunko and Lo. A 12-year-old Ethiopian boy and a 17-year-old Siberian girl join John.
- The Skid's First Voyage. They travel to the South Pacific, picking up many colleagues on the way. On arrival they take over an island, massacring the original inhabitants.
- The Colony is Founded. John and Lo briefly return to England.
- The Colony in Being. The narrator travels to the island and describes the colony.
- The Beginning of the End. The island is discovered by a British surveying vessel called the Viking. This is followed by a visit from two British light cruisers, a visit from the Soviets, and a final attempt at mass arrest by an international expedition. All are repelled with psionic attacks.
- The End. Mercenaries invade the island, but are driven away with harsh psionic attacks. On 15 December 1933, the colonists deliberately destroy their own island.
I believe you're thinking of The Chrysalids. It's a children's novel I read in 9th grade English class.
According to Wikipedia, it was written by John Wyndham and published in 1955. If you read it in the US it may have been called Re-Birth.
The story is how you describe, about a group of children who communicate telepathically and gather in New Zealand at the novel's close. The setting is post-WWIII in a dogmatic christian society that exiles mutated individuals to the nuclear wasteland.