As Charles Adler discusses in his excellent book,Aliens, Wizards and Starships, a planet residing in Earths orbit, but directly opposite from Earh on the other side of the Sun would not be possible.It turns out that such an orbit doesn’t remain stable for very long, due to the destabilizing tugs from other planets.
Historically, science fiction turned towards this troupe as it seemed safe to assume that such a planet could go undetected until some special telescope found it in the far future. It turns out that even if such an orbit were stable we would still have been able to detect the plane long ago. Though purely Earth based telescopes may indeed have trouble, we have sent probes toward the Sun that could have seen what is beyond the Sun on the other side.
Such a world was the focus of the underrated and one and only live action Gerry Anderson film, Journey to the Farside of the Sun. In addition, the menacing aliens in Gamera vs. Guiron were also from such a world (this film is usually properly rated as silly).
To read more, see my book:The Physics and Astronomy in Science Fiction.