The possibility of the control of energy spectrum and magnetization of circular quantum dots and quantum rings in a transverse magnetic field is considered.The dressing of the confining potential by an intense laser field as well as induction of Rashba spin-orbit interaction by an external electric field is shown to be effective tools for the manipulation of magnetic properties of quantum dots and rings.The temperature effect on magnetization is also considered.It is shown that the intense laser field creates an anisotropy in the system due to which the energy spectrum breaks to groups of states.The Rashba spin-orbit interaction, in its turn, creates several level anticrossings in energy spectrum.Both of these effects have their signatures on magnetization of quantum dots and rings.