Plasma parameters of magnetically confined Cobalt (Co) plasma have been evaluated by using laser-induced breakdown spectroscopy at various laser irradiances, under different ambient pressures of two environments such as Ar and Ne and at different time delays. The effect of laser irradiance on Co plasma is exposed in the presence and absence of a Transverse Magnetic field (TMF) while keeping environmental gas pressure constant, i.e., 10 Torr. For this purpose, Co pellets were exposed to Nd: YAG laser (1064 nm, 10 ns) at various laser irradiances ranging from 1 to 2.9 GW cm-2. To investigate the impact of background gas pressures, Co pellets were exposed to various pressure varying from 5 to 760 Torr of Ar and Ne. In the case of time delay variation, the Co plasma parameters Texc and ne decrease exponentially. A significantly pronounced effect of the presence of an external TMF of strength 0.9 T on time-integrated Co plasma parameters has been revealed. Plasma parameters Texc and ne are considerably increased in the presence of TMF in both ambient environments because of being constrained to a very small region due to which collisions will be enhanced. Implementation of the 0.9 T TMF on a laser-induced plasma of Co is responsible for the confinement of plasma. The surface morphology of laser-irradiated Co samples was also discussed to confirm the effect of TMF. Fine and uniform structures are observed in samples treated in the presence of TMF by using the SEM technique.