  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_rot ~ 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.
