Small nuclear collisions are mainly sensitive to cold-nuclear-matter effects; however, the collective behavior observed in these collisions shows a hint of hot-nuclear-matter effects. The identified-particle spectra, especially the ϕ mesons which contain strange and antistrange quarks and have a relatively small hadronic-interaction cross section, are a good tool to study these effects. The PHENIX experiment has measured ϕ mesons in a specific set of small collision systems p+Al, p+Au, and 3He+Au, as well as d+Au [Adare et al., Phys. Rev. C 83, 024909 (2011)], at √sNN=200 GeV. The transverse-momentum spectra and nuclear-modification factors are presented and compared to theoretical-model predictions. The comparisons with different calculations suggest that quark-gluon plasma may be formed in these small collision systems at √sNN=200 GeV. However, the volume and the lifetime of the produced medium may be insufficient for observing strangeness-enhancement and jet-quenching effects. The comparison with calculations suggests that the main production mechanisms of ϕ mesons at midrapidity may be different in p+Al versus p/d/3He+Au collisions at √sNN=200 GeV. While thermal quark recombination seems to dominate in p/d/3He+Au collisions, fragmentation seems to be the main production mechanism in p+Al collisions.