The Agnia asteroid family was recently studied by Vokrouhlický et al. because of its peculiar and, so far, unique relationship with the z1 secular resonance. The Agnia family is almost entirely contained within the high-order secular resonance z1. Here, I study another family in the middle belt that is characterized by its interaction with the z1 resonance, the Padua family. More than 75 per cent of its members are currently on z1 librating orbits, and therefore several of the techniques used by Vokrouhlický et al. can also be applied to this family. As for the case of the Agnia family, numerical integration methods and Monte Carlo models can be used to set lower and upper limits on the family age, and to obtain estimates on the fraction of prograde rotators. The constraints obtained on the family age and original ejection velocity field may be used to set limits on the dynamical mobility caused by low-energy collisions, that is dependent on the yet poorly known exponent α that best fits the size distribution of objects of less than 5 km in diameter.In this work, the Padua dynamical family was obtained in both the proper element and frequency domains. Numerical simulations of family members in the space of the z1 resonance variable (σ, dσ/dt) suggest that the family is at least 25 Myr old. The conservation of the z1 K'2 conserved quantity implies that the original ejection velocity field was of VEJ = 35.0 +/- 8.5ms-1. Monte Carlo models of the diffusion of the semimajor axis caused by the Yarkovsky and Yarkovsky-O'Keefe-Radzievsky-Paddack (YORP) effects also confirm the results obtained with the alternative approaches. The Padua family is 24+28-20Myr old, and it was probably created by an impact that ejected fragments with average ejection velocities of VEJ = 30.0+2.0-4.0ms-1. The fact that the Padua family is at least 25 Myr old suggests that low-energy collisions as modelled by Dell'Oro & Cellino should have played a minor role in the semimajor axis diffusion of the family members. My results are at best consistent with a value of α equal to -2.3. Families interacting with secular resonances such as the Agnia and Padua families can provide useful information not only about their age and original ejection velocity field, but also on the yet poorly known cumulative size distribution of objects of diameters of 5 km and less.