We present a study of short-period, central helium-burning variable stars in the Local Group dwarf spheroidal galaxy LeoI, including 106 RR Lyrae stars and 51 Cepheids. So far, this is the largest sample of Cepheids and the largest Cepheids to RR Lyrae ratio found in such a kind of galaxy. Comparison with other Local Group dwarf spheroidals, Carina and Fornax, shows that the period distribution of RR Lyrae stars is quite similar, suggesting similar properties of the parent populations, whereas the Cepheid period distribution in LeoI peaks at longer periods (P ~ 1.26 days instead of ~0.5 days) and spans over a broader range, from 0.5 to 1.78 days. Evolutionary and pulsation predictions indicate, assuming a mean metallicity peaked within –1.5 <~ [Fe/H] <~ –1.3, that the current sample of LeoI Cepheids traces a unique mix of anomalous Cepheids (blue extent of the red-clump, partially electron-degenerate central helium-burning stars) and short-period classical Cepheids (blue-loop, quiescent central helium-burning stars). Current evolutionary prescriptions also indicate that the transition mass between the two different groups of stars is M HeF ~ 2.1 M ☉, and it is constant for stars metal-poorer than [Fe/H] ~ –0.7. Finally, we briefly outline the different implications of the current findings on the star formation history of LeoI.