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In 1898 it is claimed he built the Tesla-scope  , a radio transceiver designed for communication with extraterrestrial intelligence. I say it is "claimed" he built such a device because it has never actually been proven if this is a claim based on reality, delusion or braggarts bravado.
In 1938 Tesla's long time associate and apprentice Arthur Matthews rebuilt it making it more compact and state of the art with some modernization relevant to the 1930s. In 1899 while working on his Magnifying Transmitter  he claimed to have detected coherent radio signals which he believed originated on Mars.
In 1901 he gave an interview to the magazine Colliers weekly which was published under the heading "Talking with Planets" which bares this out. 
"I can never forget the first sensations I experienced when it dawned upon me that I had observed something possibly of incalculable consequences to mankind. I felt as though I were present at the birth of a new knowledge or the revelation of a great truth.... My first observations positively terrified me, as there was present in them something mysterious, not to say supernatural, and I was alone in my laboratory at night; but at that time the idea of these disturbances being intelligently controlled signals did not yet present itself to me.... It was sometime afterward when the thought flashed upon my mind that the disturbances I had observed might be due to an intelligent control. ... The feeling is constantly growing on me that I had been the first to hear the greeting of one planet to another. A purpose was behind these electrical signals...."
In 1909 the NY Times published an article of his entitled "How to Signal Mars"  the following is an excerpt ..
"...we do not have no absolute proof that mars is inhabited ... I have my faith on the feeble planetary electrical disturbances which I discovered in the summer of 1899, and which according to my investigations, could not have originated from the Sun, the Moon, of Venus. Further study since has satisfied me they must have emanated from Mars."
So ends any published or public emanations from Tesla himself regarding extraterrestrial contact. He built huge towering magnetic transmitters in Colorado, New York and Canada but there is no record that he was ever able to initiate two way communication. He only received and listened in, attempting to interpret what his apparatus picked up.
However his long term apprentice, associate and friend who worked hand in hand with him for many years was a man named Arthur Matthews. 30 years after Teslas death Matthews published "The Wall of Light: Nikola Tesla and the Venusian Space Ship, the X-12 " which contains much of the claims regarding contact with Venusians. The book reads like a science fiction novel, but then again so did Tesla's life.
The book is touted as an Autobiography and some sources list Nikola Tesla as the Author. However - it is important to keep in mind that it was published a full 3 decades after his demise and was largely written by Arthur Matthews.
Matthews claims that he himself was taken to Venus on a ship and also was permitted to use a "Silver Ball Time Machine" they had. He also claims that the ships occupants told him that Tesla was a Venusian born on a ship that landed in Tesla's hometown in Yugoslavia on July 9 - 10 . Margaret Storms, perhaps drawing on the writings of Matthews and other occultists, paranormal and supernatural researchers in her self published book made the curious statement that Tesla was the embodiment of a superior being from the Planet Venus.
There is a drawing of a cigar shaped space craft that Tesla designed. He is alleged to have built it in 1917. Some say it resembles the Adamski UFOs [See- Bell Project - Post War Reappearance] which have not been disproven.
1. Teslascope is a term coined by a Englishman named Arthur Mathews who was Teslas long time apprentice and friend.
2. Magnifying Transmitter was the device by which Tesla transmitted energy through the atmosphere
3. Collier's Weekly, February 9, 1901, reprint
4. NY Times 1909 Reprint