Many-body interference between indistinguishable particles can give rise to strong correlations rooted in quantum statistics. We study such Hanbury Brown–Twiss-type correlations for number states of ultracold massive fermions. Using deterministically prepared atoms in optical tweezers, we measure momentum correlations using a single-atom sensitive time-of-flight imaging scheme. The experiment combines on-demand state preparation of highly indistinguishable particles with high-fidelity detection, giving access to two- and three-body correlations in fields of fixed fermionic particle number. We find that pairs of atoms interfere with a contrast close to 80%. We show that second-order density correlations arise from contributions from all two-particle pairs and detect intrinsic third-order correlations.