Extragalactic jets harbor dynamically important, organized magnetic fields. We explore with grid-adaptive, high resolution numerical simulations the morphology of AGN jets pervaded by helical field and flow topologies. We concentrate on the long term evolution of kinetic energy dominated jets, penetrating denser clouds. The jets have near-equipartition magnetic fields, and radially varying Lorentz factor profiles maximally reaching Γ ∼ 22. The helicity of the beam magnetic field is effectively transported down the beam, with compression zones in between diagonal internal cross-shocks showing stronger toroidal field. The high speed jets have localized, strong toroidal field within the backflow vortices and a more poloidal field layer, compressed between jet beam and backflows. This layer stabilizes the jet beam. We infer emission intensity, suggesting a clear trend were highly structured beams are found for toroidal fields, while inner beam cross-shocks and thin hotspots are detectable for poloidal topologies. Significant jet deceleration only occurs beyond distances exceeding $$\mathcal{O}(100{R}_{j})$$ , as the axial flow can reaccelerate downstream to the internal cross shocks. This reacceleration is magnetically aided by field compression across the internal shocks that pinch the flow.