You should start by realising that it is not possible to prove a negative. Hence, nobody can prove that your hypothetical particle doesn't exist. Nor can anybody prove that there is no god, or no fairies at the bottom of my garden.
So yes, your particles might exist. If they exist, and they obey natural laws, presumably science will discover them at some point in the future. If they don't obey natural laws then they are outside the realm of science. If you want to claim a "supernatural" object then I would suggest the onus is on you to prove its existence. And, as we are physical beings, there seems to be no way objects can affect us without using at least some of the laws of physics. That would make them non-supernatural, and hence detectable with the right equipment.
Let me add that science already recognises particles that do not seem to obey the known laws. I'm talking here about dark matter. There is a lot of evidence for it, e.g. the movement of galaxies, of stars in a galaxy, gravitational lensing, the pattern of variation in the CMB, simulations of the growth of galaxies, etc). It is generally agreed that billions of dark matter particles pass through us without any effect. Yet, all our efforts to detect them have been in vain, so far - but we keep trying. Note that dark matter does obey Newton's (and Einstein's) law.
The laws of General Relativity and Quantum Mechanics, when applied to the known particles, let us make predictions accurate to 13 decimal places. So these laws must be close to the truth. Yet we also know they cannot be the final truth, as they are incompatible with each other. When we finally come up with some form of quantum gravity these incompatibilities may disappear, and at the same time other particles, fields and forces may reveal themselves. These may be the particles you hypothesise, but their effects will only be visible beyond the 13th decimal - in other words, not in practical experience.