|MadSci Network: Physics|
As you know, we have only discovered one zero-spin (or "scalar") elementary particle so far, which is the Higgs Boson. This charge-less, spin-less particle (and its associated field) was the final, missing piece in the current Standard Model of particle physics before its discovery in 2012. This does not necessarily mean that there are no other scalar elementary particles to discover. We know that the Standard Model is an incomplete theory, and there is a lot of research at CERN and other places devoted to searches for physics beyond the Standard Model (or BSM).
There are different BSM theories being explored, and predictions of possible new scalar particles appear in many of them. For instance, instead of a single Higgs boson, theories like Supersymmetry contain multiple Higgs bosons, some of which are charged. A quick Google search for "Charged Higgs" will return lots of papers about singly- and doubly-charged Higgs bosons.
Most BSM theories also include some kind of particle like the Leptoquark, which can transform quarks into leptons and vice-versa. Leptoquarks would have non-integer charges, and both scalar and vector (spin-1) leptoquarks are hypothetically possible. So this is another possible kind of charged scalar particle. Again, a Google search will bring up a lot more information.
Hope this helps!
P.S. I forgot to add, you are correct that it is possible for composite particles to have zero net spin and charge. An example would be atoms in a Bose-Einstein condensate.
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