The idea of creating magnetically controllable colloids whose rheological properties can be finely tuned on the nano- or micro-scale has caused a lot of experimental and theoretical effort. The latter resulted in systems whose building blocks are ranging between single magnetic nanoparticles to complexes of such nanoparticles bound together by various mechanisms. The binding can be either chemical or physical, reversible or not. One way to create a system that is physically bound is to let the precrosslinked supracolloidal magnetic polymers (SMPs) to cluster due to both magnetic and Van-der-Waals-type forces. The topology of the SMPs in this case can be used to tune both magnetic and rheological properties of the resulting clusters as we show in this work. We employ Molecular Dynamics computer simulations coupled with explicit solvent modelled by Lattice-Boltzmann method in order to model the behaviour of the clusters formed by chains, rings, X- and Y-shaped SMPs in a shear flow with externally applied magnetic field. We find that the shear stabilises the shape of the clusters not letting them extend in the direction of the field and disintegrate. The clusters that show the highest response to an applied field and higher shape stability are those made of Y- and X-like SMPs. © 2023 Elsevier B.V.