New star cluster candidates projected toward the Large and Small Magellanic Clouds (LMC, SMC) have been recently discovered from relatively deep imaging surveys. Here, we conduct a sound analysis of 24 star cluster candidates located in the outer regions of the LMC and SMC using point spread function photometry produced by the Survey of the Magellanic Stellar History. With only one exception, the studied objects were shown to be genuine stellar aggregates. We drew our conclusions on their physical characteristics once their observed color-magnitude diagrams (CMDs) were statistically decontaminated by the presence of field stars. The resulting cleaned CMDs, for stars with assigned membership probabilities higher than 50%, were compared with synthetic CMDs generated for thousands of combinations of ages, distances, metallicities, star cluster masses, and binary fractions. The parameters of the best-matched synthetic CMDs obtained from a likelihood approach were adopted as the star cluster astrophysical properties. The present star cluster sample spans a wide range of distances, from those star clusters located in front of the LMC through those along the onset of the Magellanic Bridge up to those behind the SMC. Their ages reveal different formation episodes that took place over the course of galaxy formation and others as a consequence of interactions among galaxies. From their estimated metallicities and ages, we speculate on the possibility that relatively metal-deficient gaseous flows have existed between these galaxies during nearly the last one Gyr (log(age yr−1) ≈ 9.0), which facilitated the formation of young star clusters in the galaxy peripheries. Despide the LMC-SMC interactions, the studied star clusters are similar or more massive than their counterparts in the Milky Way, suggesting that tidal effects are relatively more important in our Galaxy.