I think, that thinking about these as "elements" instead of compounds is fundamentally flawed.
The list of elements is pretty fixed an pretty well known, it's governed by the weak nuclear force and how it binds atomic nuclei together. This governs how stable a given element is and what its atomic number is. A brief and simplified description of the weak force and the stability of atomic nuclei, is that the proton has positive charge. Like charges repel so when you get so many protons packed together their positive charges [repulsion] can overcome the binding force of the weak nuclear force. When this happens the atom breaks apart in what we call radiation (typically alpha decay through fission). Adding more neutrons can separate the protons enough to keep the atom stable as neutrons add the weak force but are electrically neutral. This only works up to a certain point, after that the atom becomes unstable in relatively small time frames. This upper stability limit is Lead at atomic number 82. Uranium (92) and Plutonium (94) sit beyond this. Plutonium is very hard to find naturally as it's half life(80.3 million years) is low enough that most if not all of the Plutonium from the creation of the solar system has decayed into lighter elements like lead or uranium. Elements higher then Uranium are often called transuranic elements, and don't exist in nature as any that did would have decayed away by now.
Most of these we have manufactured in particle accelerators and some nuclear reactions and some of them tend to decay in fractions of a second that you need scientific notation to measure. These could be a source of some exotic elements, if you could justify their stability. One possibility way to do this would be to have a very young solar system. However, these may not be "exotic" enough, because even though we don't know much about them, we do know a fair bit.
So you can see the way elements are build and what limits them is well understood. It's hard to reason into being some element we could have "missed" with these magic properties, without some hand waving. Well at least for people that have some grasp of nuclear physics.
Possibly a much better bet is compounds or molecules that are exotic. There is a much wider range here, they are less fixed and you can have all kinds of alloys and things that have special properties (meta materials etc). These would be molecules instead of elements. Which may or may not seem to be a big distinction, but it is. So you could probably get a way with some type of exotic ore that has special properties as long as it's not an "element". This could be from a meteorite strike, formation in space uses different conditions then formation on a planet.
The only elemental possibility I can think of is the so called Island of stability.
Which basically postulates that certain high atomic numbers are "magical" and the resulting heavy element would be stable for day, weeks, years or even longer. I haven't done much research into this area, but as far as I know we haven't found any evidence that this is true. In any case you could have some kind of deposit of this "unobtainium" that loosely conformed to the ideas for this.
I think any kind of exotic substance like this requires some amount of hand waving.
When I write about technology and things that are a bit on the edge of what is realistic, I intentionally leave it a bit vague. Over explaining can be a bigger problem then just leaving it up to the readers imagination. Basically you can say things that are impossible in nature, which no matter how well you reason it is still hand waving, or you can leave it a bit vague and let the reader fill in some of those blanks.