We here investigate , by means of fully three-dimensional ( 3-D ) Smoothed Particle Magnetohydrodynamic ( SPMHD ) numerical simulations , the effects of different initial magnetic field configurations on the evolution of overdense , radiatively cooling , pulsed jets , using different initial magnetic field topologies : ( i ) a longitudinal , ( ii ) a helical geometry permeating both the jet and the ambient medium , and ( iii ) a purely toroidal geometry permeating the jet only . We explore the effects of different pulsational periods , as well as different values of the magnetic field strength ( \beta \simeq 0.1 - \infty , or B \simeq 260 \mu G-0 ) . The presence of a helical or a toroidal field tends to affect more the global characteristics of the fluid than a longitudinal field . However , the relative differences which have been previously detected in 2-D simulations involving distinct magnetic field configurations are diminished in the 3-D flows . While the presence of toroidal magnetic components can modify the morphology close to the jet head inhibiting its fragmentation in the early evolution of the jet , as previously reported in the literature , the impact of the pulsed-induced internal knots causes the appearance of a clumpy , complex morphology at the jet head ( as required by the observations of Herbig-Haro jets ) even in the MHD jet models with helical or toroidal configurations . The detailed structure and emission properties of the internal working surfaces can be also significantly altered by the presence of magnetic fields . The increase of the magnetic field strength ( decrease of \beta ) improves the jet collimation , and amplifies the density ( by factors up to 1.4 , and 4 ) and the H \alpha intensity ( by factors up to 4 , and 5 ) behind the knots of jets with helical field and \beta \simeq 1 - 0.1 ( respectively ) , relative to a non-magnetic jet . As a consequence , the corresponding I _ { { [ S~ { } II ] } } / I _ { { H } \alpha } ratio ( which is frequently used to determine the excitation level of HH objects ) can be largely decreased in the MHD models with toroidal components relative to non-magnetic calculations . We also find that the helical mode of the Kelvin-Helmholtz instability can be triggered in MHD models with helical magnetic fields , causing some wiggling of the jet axis . No evidence for the formation of the nose cones that are commonly detected in 2-D jet simulations with initial toroidal magnetic fields , is found in the 3-D flows , nor even in the \beta \simeq 0.1 case . The implications of our results for Herbig-Haro jets are briefly discussed .