We theoretically investigate the generation and Josephson current signatures of Floquet Majorana end modes (FMEMs) in a periodically driven altermagnet (AM) heterostructure. Considering a one-dimensional (1D) Rashba nanowire (RNW) proximitized to a regular $s$-wave superconductor (SC) and a $d$-wave AM, we generate both 0- and $\pi$-FMEMs by driving the nontopological phase of the static system. Interestingly, the static counterpart hosts both topological Majorana zero modes (MZMs) and inquisitive nontopological accidental zero modes (AZMs) not originating from any metal-SC interface but rather intrinsic to the bulk of the isolated system. The periodic drive can gap out the static AZMs and generate robust $\pi$-FMEMs, termed as topological AZMs. We topologically characterize the emergent FMEMs via dynamical winding numbers exploiting chiral symmetry of the system. Moreover, we consider a periodically driven Josephson junction comprising a RNW/AM-based 1D topological superconduting setup. We identify the signature of MZMs and FMEMs utilizing the $4\pi$-periodic Josephson effect, distinguishing them from trivial AZMs exhibiting $2\pi$ periodicity, in both static and driven platforms. This Josephson current signal due to Majorana modes survives even in the presence of finite disorder. Our Letter establishes a route to realize and identify FMEMs in AM-based platforms through Floquet engineering and Josephson current response.

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• Josephson effect
• Majorana bound states
• Proximity effect
• Topological superconductors
• Altermagnets
• Floquet systems
• Nanowires