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We demonstrate the generation of Coulomb-correlated pair, triple and quadruple states of free electrons by femtosecond photoemission from a nanoscale field emitter inside a transmission electron microscope. Event-based electron spectroscopy allows a spatial and spectral characterization of the electron ensemble emitted by each laser pulse. We identify distinctive energy and momentum correlations arising from acceleration-enhanced interparticle energy exchange, revealing strong few-body Coulomb interactions at an energy scale of about two electronvolts. State-sorted beam caustics show a discrete increase in virtual source size and longitudinal source shift for few-electron states, associated with transverse momentum correlations. We observe field-controllable electron antibunching, attributed primarily to transverse Coulomb deflection. The pronounced spatial and spectral characteristics of these electron number states allow filtering schemes that control the statistical distribution of the pulse charge. In this way, the fraction of specific few-electron states can be actively suppressed or enhanced, facilitating the preparation of highly non-Poissonian electron beams for microscopy and lithography, including future heralding schemes and correlated multi-electron probing.