Dystopian future with telepathic children

This is John Wyndham's The Chrysalids (1955).

Set in a post-apocalyptic Labrador, the protagonist David and his telepathic friends try to hide their abilities from their rabidly anti-mutant neighbours. His younger sister Petra is a strong enough telepath to reach all the way around the world to New Zealand, where a society of telepaths are growing.

They are betrayed and two of them are captured and tortured, but ultimately David, Rosalind and Petra are taken away to "Sealand," while Michael stays behind to try to free Rachel, the last one stuck in hiding. You can read a more complete summary on the Wikipedia page.

Allowing for a lot of distortion in memory over the last 40 years, perhaps you might be thinking of Howard Fast's short story, The First Men (1960)?

It's not a great match, but it does feature a dystopic gov't (of the period appropriate Dr. Strangelove variety though, not the future), a small group of children with telepathic ability whose abilities are kept secret from all but the adults running the community (though initially only the adults raising them know how important it is to preserve the secret), and near the end they start finding more children across the world to recruit into their Utopian community of, effectively, child demigods.