  Heavy Quarks (HQs) serve as excellent probes to understand various
characteristics of deconfined hot QCD medium, comprising light quarks and
gluons, created in the Heavy Ion Collisions (HICs). Strong magnetic fields in
non-central HICs may significantly affect HQ dynamics in this medium. Exploring
the impact of the magnetic field on the perturbative and non-perturbative
transport coefficients of HQ is an intriguing endeavor. This necessitates the
development of a comprehensive theoretical framework accommodating the
non-perturbative Quantum Chromo Dynamics(npQCD) description alongside
perturbative QCD(pQCD). The present work provides such a formulation in which
Quarkonium potential in the hot and magnetic QCD medium is implemented as the
effective gluon propagator to calculate the rate of elastic scattering between
HQ and the light partons inside a medium of hot Quark Gluon Plasma(QGP) in the
presence of a strong but uniform magnetic field. Diffusion coefficients of a
charm quark have been computed for a short-range Yukawa potential ( pQCD) as
well as a long-range confining/non-perturbative potential (npQCD) for two cases
in which the velocity of the charm quark is parallel and perpendicular to the
magnetic field respectively. Non-perturbative contribution is seen to dominate
over the perturbative one in the regime of low temperatures and low to
intermediate momenta of charm quark. As the momentum of charm quark as well as
the temperature of the medium increase pQCD starts to gain on the npQCD
contribution, ultimately prevailing at higher temperatures and charm momenta.
