The 57 were detained in six different provinces, with over 100 arrest warrants issued, the state-run Anadolu news agency said. Efforts to detain the remaining suspects are in progress, it added.
They are suspected of links to the group of Fethullah Gulen, the US-based preacher Ankara accuses of being behind the failed plot to oust President Recep Tayyip Erdogan, it said. Gulen denies the charges.
The Haberturk daily said on its website that those held were former employees of the stock exchange suspected of using a encrypted messaging application called Bylock which Turkey claims was especially created for Gulen supporters.
Some 47,000 people have been arrested under the state of emergency imposed after the coup, while tens of thousands more have lost their jobs.
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Late last month, Turkey dismissed almost 4,000 public officials under the state of emergency while over 9,100 police were suspended on April 26.
The latest move underlines that there is to be no let-up in the anti-Gulen purge after Erdogan won a April 16 referendum on expanding his powers.
Turkey's Western allies, led by the European Union, have expressed concern over the magnitude of the post-coup purge which has affected every walk of life in Turkey.