It is relatively certain there are undetected planets beyond the orbit of Pluto. The discovery of Pluto, remember, was by Clyde Thombaugh, who was looking for a celestial body capable of perturbing the orbit of Neptune. However, more recent measurements of the mass of Pluto indicate that it alone can't be responsible for these perturbations, hence Neptune's irregular orbit is still unexplained, hence there are probably 1 or more undetected planets beyond the orbit of Pluto.
However, it is also relatively certain that none of these undetected planets penetrate the Solar System anywhere near the Earth. If they did, then they couldn't be responsible for perturbing the orbit of Neptune b/c the apogee of such an orbit-- its farthest point from the Sun-- would be far beyond the orbit of Pluto, & the velocity of Planet X near its apogee would be very low, so it would spend most of its time out there-- 'way too far away to have any effect on Neptune.
...so yes, these bodies almost certainly do exist; but no, they could never affect the Earth in any way.
...but-- leaving aside Neptune & Pluto-- is it possible for a massive body to exist that occupies a highly elliptical orbit that brings it close enough to the Earth every thousand years or so to cause disruption? Possible? Yes. However, we have absolutely zero evidence for it.