Hypothetical trans-Neptunian planets orbiting the Sun
If such a planet exists, WISE should observe it. WISE is an infrared satellite that imaged the entire sky. In particular:


it was able to detect anything with a temperature above 70-100 K, whereas the coolest known exoplanets are in the 100 K range (see histogram below, taken from the Exoplanets Catalogue);
it was able to detect objects larger than 1km up to 3 AU from the Sun, or objects of 2-3 Jupiter masses in a distance up to 7-10 light-years (so roughly up to 440,000 to 630,000 AU, see here and here);


so I would say that its existence is quite ruled out now.