The focus of experimental efforts on topological superconductivity (Tsc) has predominantly centered around the detection of Majorana boundary modes. On the contrary, the experimental features arising from the band topology in the bulk remain relatively unexplored. In this talk, I will discuss how spectroscopic properties away from the boundaries can be influenced by the Berry curvatures (BC) of Bogoliubov quasiparticle in a chiral p-wave Tsc achieved by spin-orbit coupling. Beyond the more well-known momentum-space BC effect, I will show that a new phase-space BC term emerges under an applied magnetic field, exclusively when the spin-orbit coupling and superconductivity coexist. Importantly, this novel BC term leads to qualitative modifications in energy- and momentum-resolved tunneling spectroscopy. Such a BC effect can be sizably amplified by the strength of spin-orbit coupling and the applied field, offering a new potentially detectable experimental feature in a chiral p-wave Tsc.