The ion heating mechanism in the context of laser interacting with plasma immersed in a strong magnetic field is studied. The electron motion transverse to the magnetic field gets restricted, and it acquires comparatively less energy than the ions. The magnetic field is chosen to be strong for laser electromagnetic field propagation inside the plasma to be governed by the magnetized dispersion relation. Both X and RL mode configurations have been studied in detail using Particle-In-Cell (PIC) simulations. It is shown that the energy absorption process is governed by a resonant mechanism wherein the laser frequency matches with an underlying mode in the plasma. For X and RL mode configurations, these correspond to lower hybrid and ion cyclotron resonance, respectively. The absorption, however, is found to be most efficient at frequencies close to but not exactly matching with the resonance frequency. An understanding of the same has been provided. The role of laser polarization has been studied in detail.