  Periodically driven quantum systems host exotic phenomena which often do not
have any analog in undriven systems. Floquet prethermalization and dynamical
freezing of certain observables, via the emergence of conservation laws, are
realized by controlling the drive frequency. These dynamical regimes can be
leveraged to construct quantum memories and have potential applications in
quantum information processing. Solid state and cold atom experimental
architectures have opened avenues for implementing local Floquet engineering
which can achieve spatially modulated quantum control of states. Here, we
uncover the novel memory effects of local periodic driving in a nonintegrable
spin-half staggered Heisenberg chain. For a boundary-driven protocol at the
dynamical freezing frequency, we show the formation of an approximate strong
zero mode, a prethermal quasi-local operator, due to the emergence of a
discrete global $\mathbb{Z}_2$ symmetry. This is captured by constructing an
accurate effective Floquet Hamiltonian using a higher-order partially resummed
Floquet-Magnus expansion. The lifetime of the boundary spin can be
exponentially enhanced by enlarging the set of suitably chosen driven sites. We
demonstrate that in the asymptotic limit, achieved by increasing the number of
driven sites, a strong zero mode emerges, where the lifetime of the boundary
spin grows exponentially with system size. The non-local processes in the
Floquet Hamiltonian play a pivotal role in the total freezing of the boundary
spin in the thermodynamic limit. The novel dynamics of the boundary spin is
accompanied by a rich structure of entanglement in the Floquet eigenstates
where specific bipartitions yield an area-law scaling while the entanglement
for random bipartitions scales as a volume-law.
