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Context. Protostellar jets are an important agent of star formation feedback, tightly connected with the mass-accretion process. The history of jet formation and mass ejection provides constraints on the mass accretion history and on the nature of the driving source. Aims. We characterize the time-variability of the mass-ejection phenomena at work in the class 0 protostellar phase in order to better understand the dynamics of the outflowing gas and bring more constraints on the origin of the jet chemical composition and the mass-accretion history. Methods. Using the NOrthern Extended Millimeter Array (NOEMA) interferometer, we have observed the emission of the CO 2–1 and SO N J = 5 4 –4 3 rotational transitions at an angular resolution of 1.0″ (820 au) and 0.4″ (330 au), respectively, toward the intermediate-mass class 0 protostellar system Cep E. Results. The CO high-velocity jet emission reveals a central component of ≤400 au diameter associated with high-velocity molecular knots that is also detected in SO, surrounded by a collimated layer of entrained gas. The gas layer appears to be accelerated along the main axis over a length scale δ 0 ~ 700 au, while its diameter gradually increases up to several 1000 au at 2000 au from the protostar. The jet is fragmented into 18 knots of mass ~10 −3 M ⊙ , unevenly distributed between the northern and southern lobes, with velocity variations up to 15 km s −1 close to the protostar. This is well below the jet terminal velocities in the northern (+ 65 km s −1 ) and southern (−125 km s −1 ) lobes. The knot interval distribution is approximately bimodal on a timescale of ~50–80 yr, which is close to the jet-driving protostar Cep E-A and ~150–20 yr at larger distances >12″. The mass-loss rates derived from knot masses are steady overall, with values of 2.7 × 10 −5 M ⊙ yr −1 and 8.9 × 10 −6 M ⊙ yr −1 in the northern and southern lobe, respectively. Conclusions. The interaction of the ambient protostellar material with high-velocity knots drives the formation of a molecular layer around the jet. This accounts for the higher mass-loss rate in the northern lobe. The jet dynamics are well accounted for by a simple precession model with a period of 2000 yr and a mass-ejection period of 55 yr.