There is an idea, first proposed thousands of years ago by Greek philosopher Philolaus, that behind the Sun where we can't see it there lurks a "counter-Earth", named Antichthon.
The theory, strange as it seems today, was likely created as a way to explain lunar eclipses. Lunar eclipses are more frequent than solar eclipses, and according to Aristotle it was believed that this was because some lunar eclipses were caused by the interposition of this counter Earth. In this view of the Solar System, the Earth and the Sun rotate around an unseen "central fire", with Antichthon on the other side of it to us, sometimes casting its shadow on the Moon.
Another reason, even less scientific, was that Antichthon brought the total moving body count up to ten, a number pleasing to the Pythagoreans.
When we moved away from Earth-centric views of the Solar System, this theory died away. However, in modern times it has sometimes reared its head as a conspiracy theory, where the planet is hiding on the other side of the Sun.
Amazingly, this kind of orbit is possible, and one such system may have been detected.
As the planets share the same orbit, conditions could be similar.
“Who could imagine two worlds that share the duration of the year and the habitability conditions? Our work is the first evidence that this kind of world could exist,” lead author Olga Balsalobre-Ruza said in a statement. “We can imagine that a planet can share its orbit with thousands of asteroids as in the case of Jupiter, but it is mind-blowing to me that planets could share the same orbit.”
However, this isn't happening in our Solar System. While it's a fun idea for sci-fi to imagine ourselves in a similar situation without realizing it, just because we cannot directly see behind the Sun doesn't mean we don't know what's going on back there. We can see planets by how they influence others. In fact, that's how we found Neptune, by observing that Uranus's orbit was being influenced by an unknown planet beyond it.
We haven't seen any orbit perturbations that would imply a planet is hiding from us. One experiment looked at the orbits of the planets if an "anti-Earth" dubbed "Clarion" was added into our current models, finding that it would quickly be disturbed by the orbit of Venus, and become visible to us.
"During the 112 years covered by the integration the separation becomes large enough in all cases that Clarion should have been directly observed, particularly at times of morning or evening twilight and during total solar eclipses," the authors concluded in the study. "The most obvious effect of the presence of Clarion, however, is its influence on the positions of the other planets. During the past 150 years precise observations by means of meridian circles have been made of the motions of the principal planets of the Solar System. Differences introduced, by the presence of an anti-Earth (Clarion) of non-negligible mass, in the motions of Venus, Earth, and Mars could not have remained undetected in this period."
Supposing it had a way to defy physics, it should still have been visible to NASA’s Solar Terrestrial Relations Observatory when its satellites were angled to see beyond the Sun. They found, of course, nothing.