<p>High-harmonic generation and ultrafast electron coherent control are central goals in modern strong-field physics. However, the problem of producing and manipulating electron-matter-wave pulses at zeptosecond timescales remains a major challenge. Here we investigate the quantum dynamics of relativistic electrons (in general, spin-1/2 fermion particles) at the inelastic Cherenkov diffraction on a slowed in a dielectric/gaseous medium laser pulse phase-lattice. Using a relativistic quantum kinetic approach, we show that multiphoton absorption-radiation up to <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(10^4\)</EquationSource> </InlineEquation> photons leads to strong temporal compression of the electron initial wave packet. After the free-space propagation of electron matter wave-partial-sub-packets, formed at the inelastic diffraction scattering on the laser pulse phase-lattice, the attosecond-zeptosecond electron pulse trains structure establishes. We demonstrate that such compression of matter wave-pulse duration is robust to laser pulse duration but sensitive to the momentum spread of the beam. Our findings establish a pathway towards the creation of tabletop zeptosecond electron sources (with several tens of MeV energies from microtrons) for ultrafast quantum control, time-resolved spectroscopy, and high-resolution electron microscopy, as well as, wide applications in relativistic microelectronics.</p>