  Recent observations of several massive pulsars, with masses near and above
$2~M_\odot$, point towards the existence of matter at very high densities,
compared to normal matter that we are familiar with in our terrestrial world.
This leads to the possibility of appearance of exotic degrees of freedom other
than nucleons inside the core of the neutrons stars (NS). Another significant
property of NSs is the presence of high surface magnetic field, with highest
range of the order of $\sim~10^{16}$ G. We study the properties of highly dense
matter with the possibility of appearance of heavier strange and non-strange
baryons, and kaons in presence of strong magnetic field. We find that the
presence of a strong magnetic field stiffens the matter at high density,
delaying the kaon appearance and, hence, increasing the maximum attainable mass
of NS family.
