In recent times, the higher-order topological (HOT) phases, harboring boundary modes of lower dimensions than their usual ones, have been proposed with unconventional bulk-boundary correspondence. We have come up with a general framework to construct the HOT insulator [1] and superconductor (with s-wave superconductivity) [2] phases, preserving unitary chiral and anti-unitary particle-hole symmetries, with appropriate Wilson-Dirac masses. We periodically kick these mass terms to generate the ladder of HOT phases that are only protected by the anti-unitary particle-hole symmetry while the static system remains in the lower-order topological or trivial phase [1,2]. We characterize these static and dynamic HOT phases with suitable topological invariants namely, quadrupolar moment, octupolar moment, and Wannier spectra. Apart from zero energy regular HOT modes, we also find finite energy anomalous HOT modes [3,4]. At the end, we connect it to the recent experimental findings to highlight the relevance of this field.