Seismic aftershock‐hazard analysis is one of the first steps toward establishing an integrated risk‐based decision‐making support framework for emergency management in the event of an ongoing aftershock sequence. This work focuses on providing adaptive daily forecasts of the mean daily rate of exceeding various spectral acceleration values (the aftershock hazard). Two well‐established earthquake‐occurrence models suitable for daily seismicity forecasts associated with the evolution of an aftershock sequence, namely, the modified Omori’s aftershock model (MO) and the epidemic‐type aftershock sequence (ETAS) are adopted. An adaptive and evolutionary MO‐based aftershock occurrence model with distinct spatial and temporal components is proposed. In this model, the parameters deciding the temporal decay are updated based on the data provided by the ongoing aftershock sequence. This model adopts an evolutionary spatial seismicity pattern loosely based on spatial clustering of aftershock events in the sequence. Bayesian updating is also employed to provide sequence‐based parameter estimates for a given ground‐motion prediction model. Daily forecasts of the mean rate of exceedance of various spectral acceleration levels are calculated based on alternative occurrence models and the updated ground‐motion prediction relation. As a numerical example, daily forecasts of the aftershock‐hazard curve are obtained for the L’Aquila aftershock sequence based on the MO‐based and ETAS occurrence models, and an updated version of the Sabetta and Pugliese (1996) ground‐motion prediction model. These daily hazard forecasts are then compared with the observed daily rates of exceeding various spectral acceleration thresholds.