We present four new light curves of transiting exoplanets WASP-1b and HAT-P-20b , observed within the TASTE ( The Asiago Search for Transit timing variations of Exoplanets ) project . We re-analyzed light curves from the literature in a homogeneous way , calculating a refined ephemeris and orbital-physical parameters for both objects . WASP-1b does not show any significant Transit Timing Variation signal at the 120 s-level . As for HAT-P-20b , we detected a deviation from our re-estimated linear ephemeris that could be ascribed to the presence of a perturber or , more probably , to a previously unnoticed high level of stellar activity . The rotational period of HAT-P-20 A we obtained from archival data ( P _ { \mathrm { rot } } \simeq 14.5 days ) , combined with its optical variability and strong emission of CaII H & K lines , is consistent with a young stellar age ( < 1 Gyr ) and support the hypothesis that stellar activity may be responsible of the measured deviations of the transit times .