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B and V time-series photometry of the M31 dwarf spheroidal satelliteAndromeda XXI (And XXI) was obtained with the Large Binocular Cameras at theLarge Binocular Telescope. We have identified 50 variables in And XXI, of which41 are RR Lyrae stars (37 fundamental-mode RRab, and 4 first-overtone RRc,pulsators) and 9 are Anomalous Cepheids (ACs). The average period of the RRabstars (<Pab> = 0.64 days) and the period-amplitude diagram place And~XXI in theclass of Oosterhoff II - Oosterhoff-Intermediate objects. From the averageluminosity of the RR Lyrae stars we derived the galaxy distance modulus of(m-M)$_0$=$24.40\pm0.17$ mag, which is smaller than previous literatureestimates, although still consistent with them within 1 $\sigma$. The galaxycolor-magnitude diagram shows evidence for the presence of three differentstellar generations in And~XXI: 1) an old ($\sim$ 12 Gyr) and metal poor([Fe/H]=$-$1.7 dex) component traced by the RR Lyrae stars; 2) a slightlyyounger (10-6 Gyr) and more metal rich ([Fe/H]=$-$1.5 dex) component populatingthe red horizontal branch, and 3) a young age ($\sim$ 1 Gyr) component withsame metallicity, that produced the ACs. Finally, we provide hints that And~XXIcould be the result of a minor merging event between two dwarf galaxies.

Variable stars and stellar populations in Andromeda XXI: II. Another merged galaxy satellite of M31?