  Emission properties of compact astrophysical objects such as Neutron stars
(NSs) are associated with crucial astronomical observables. In the current
work, we obtain the mass, pressure profiles of the non-rotating NSs using the
modified Tolman Oppenheimer Volkoff (TOV) system of equations in the presence
of intense magnetic field. We obtain the profiles by using a specific
distance-dependent magnetic field in the modified TOV equations. We employ
three different equations of states (EoS) to solve the TOV equations by
assuming the core of NSs comprises a hadronic matter. Employing the above
profiles, we determine the cooling rates of spherically symmetric NSs as a
function of time with and without including the magnetic field using the NSCool
code. We have also determined the cooling rates as a function of radius for
three different NSs. Furthermore, we determine the luminosity of neutrinos,
axions, and photons emitting from the NSs in the presence and absence of a
magnetic field for an axion mass $16$ meV and three different EoS. Our
comparative study indicates that the cooling rate and luminosities of
neutrinos, axions, and photons change significantly due to the impact of the
strong magnetic field. We also find that due to the magnetic field, the axion
mass bound increases slightly compared to without a magnetic field..
