Imaginary planets have always intrigued both, astronomers and layman, stimulating people’s creativity and encouraging scientific research.
Tyche for instance went in the history as a planet that was believed to be located in the Oort Cloud and was believed to have an impact of on the movement of comets.
The Counter-Earth was an earliest myth that was a supposed second copy of the Earth located on the other side of the sun which cannot be observed. Based on the difficulties these theories failed to explain, vulcan was hypothesized in the nineteenth century to exist between Mercury and Sun in order to mend these irregularities seen in Mercury.
But there are many others; and they are as strange as these I have enumerated!

As we have already mentioned, they have never been discovered; however, let us imagine how they would affect the Solar system, if they did!