If you disturb an atom, you can knock off some of the electrons. Usually, this is done just by heating your sample; you can also use high-frequency light or other methods. When you do this, the atom gains a charge.
If you heat up a hydrogen atom, you can give it a certain charge, no more nor less. We call that charge +1. If you heat up helium, you can give it this same amount of charge, and if you heat it up more, you can give it exactly twice as much, but no other amount. In other words, you can give it a charge of +1 or +2. Likewise, you can give lithium a charge of +1, +2, or +3, and so on. The simplest explanation for this is that a hydrogen atom has exactly one electron, a helium atom has two, which can be knocked off one at a time, etc.
It is certainly possible that the electron is actually a composite particle of some sort, and therefore that when you knock off an electron, you’re actually knocking off two or more smaller particles. But there’s no indication at all that this is true, and even if it is, it’s certainly very difficult to separate those particles, so one can still call an electron a particle.
By definition, two atoms are the same element if they have the same amount of protons, so for every number of protons, there is one and only one element. We have discovered all of the elements corresponding to numbers from one to past a hundred. The only way you could get any other elements would be to go out to even higher numbers, or to have a fractional number of protons. Although protons are composite particles made up of three quarks, and a quark might therefore be said to be a third of a proton, all indications are that it’s absolutely impossible to separate out individual quarks. And for elements higher than 100, some are more stable than others, but even at best, you’re looking at half-lifes of a few seconds, so we shouldn’t expect to find any in deep space unless we stumble across some natural phenomenon which is continually producing them. Your best bet for finding non-Earthly substances is to suppose some new form of a known element or combinations of known elements (a different isomer, say, or a new chemical compound), or a substance which is so unlike familiar materials that it is not made up of atoms at all.