  We consider our recently obtained general structure of two point (self-energy
and propagator) functions of quarks and gluons in a nontrivial background like
a heat bath and an external magnetic field. Based on this, here we have
computed free energy and pressure of quarks and gluons for a magnetized hot and
dense deconfined QCD matter in weak field approximation. For heat bath we have
used hard thermal loop perturbation theory (HTLpt) in presence of finite
chemical potential. For weak field approximations we have obtained the pressure
of QCD matter, both with and without the high temperature expansion. The
results with high $T$ expansions are completely analytic and gauge independent
but depends on the renormalization scale in addition to the temperature,
chemical potential and the external magnetic field. We also discuss the
modification of QCD Debye mass of such matter for an arbitrary magnetic field.
Analytic expressions for Debye mass are also obtained for both strong and weak
field approximation. It is found to exhibit some interesting features depending
upon the three different scales, i.e, the quark mass, temperature and the
strength of the magnetic field. The various divergences appearing in the quark
and gluon free energies are regulated through appropriate counter terms. In
weak field approximation, the low temperature behavior of the pressure is found
to strongly depend on the magnetic field than that at high temperature. We also
discuss the specific problem with one-loop HTLpt associated with the
over-counting of certain orders in coupling.
