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Star Trek: TOS (1966) TV series showed such device long before mobile phones came into existence, but was it the first?

In 1926, Tesla envisioned mobile phones even better than Star Trek:

There seems a huge gap between 1926 and 1966 if Star Trek was really the first. Also, we have Jules Vernes and H. G. Wells type writers who predicted atom bomb, moon landing etc in great detail. So, it is possible that someone wrote about handheld wireless communicators before 1926.

Which Sci-Fi work introduced handheld wireless communicator?

The earliest example I can find of a hand-held 2-way electronic communications device is Dick Tracy's 2-way wrist radio which appeared in the Dick Tracy comic strip on January 13, 1946.

There must be many earlier stories that involve communications by magical (or other non-scientific) means.

1936: "Finality Unlimited", a novella by Donald Wandrei, first published in Astounding Stories, September 1936, available at the Internet Archive. The story is set (initially) on August 28, 2005:

Despite the heat, an air of excitement prevailed on the streets and the hanging-garden cafes. The Second Expedition to Mercury should land at any time now with news of what happened to the First Expedition, still missing from its maiden voyage years ago in 1991.

The arteries and towers of Manhattan had begun to assume the aspect of a dream city, as the products of science came into wider use. The race was
markedly happier, healthier, taller than a century before; the atmosphere filtered of dirt and gases; the harbors clean again; life a richer and broader experience. Each individual carried an identification tag, and a pocket radiophone that permitted conversation with any one anywhere on the globe.

[. . . .]

Stanley King had dressed and begun packing when he heard the signal of his pocket radiophone. He hesitated about answering it. He didn't want to get tangled with anything that might delay his departure. Still, it might be a call of importance, and finally he answered with a noncommittal, "Yes?"

1930: "Mr. Murphy of New York", a short story by Thomas McMorrow; first published in the March 22, 1930 issue of The Saturday Evening Post; also the answer to the story-ID question Story about leaving the bath running/skyscraper collapse.

"Now, gentlemen, please," breathed Mr. Bligh. "Do remember that I'm a thousand miles from home and haven't had any lunch yet. Well, I shall have to call up." He took out his pocketell. "Are you there? Billy calling . . . Hello, Molly! I just called you to say that I can't possibly get home— What's that, sweetheart? . . . Oh, no, no. . . . But I say that I am not! I am in New York in a conference. . . . Yes, business. . . . Why don't I— Now, Molly, how can you ask me to be so rude? . . . Oh, very well, my dear, in a moment." He turned to us, coloring, and said, "Will you permit?" We were married men ourselves; we smiled and got to our feet and bowed to his lady when she appeared; her eyes swept us vigilantly. "I'm sorry this had to happen, gentlemen," said Mr. Bligh, blanking her. "May we proceed now with our affair?"

A character in Heinlein's 1948 novel Space Cadet tells his friend something to the effect "I wish I had her cell number". I will update in morning when I can find the page.