ABSTRACT Asymmetric debris discs have been found around stars other than the Sun; asymmetries are sometimes attributed to perturbations induced by unseen planets. The presence or absence of asymmetries in our own trans-Neptunian belt remains controversial. The study of sensitive tracers in a sample of objects relatively free from the perturbations exerted by the four known giant planets and most stellar flybys may put an end to this debate. The analysis of the distribution of the mutual nodal distances of the known extreme trans-Neptunian objects (ETNOs) that measure how close two orbits may get to each other could be such a game changer. Here, we use a sample of 51 ETNOs together with random shufflings of this sample and two unbiased scattered-disc orbital models to confirm a statistically significant (62σ) asymmetry between the shortest mutual ascending and descending nodal distances as well as the existence of multiple highly improbably (p < 0.0002) correlated pairs of orbits with mutual nodal distances as low as 0.2 au at 152 au from the Solar system’s barycentre or 1.3 au at 339 au. We conclude that these findings fit best with the notion that trans-Plutonian planets exist.