Proton irradiations are highly sensitive to spatial variations, mainly due to their high linear energy transfer (LET) and densely ionizing nature. In realistic clinical applications, the targets of ionizing radiation are inhomogeneous in terms of geometry and chemical composition (i.e., organs in the human body). One of the main methods for proton range monitoring is to utilize the production of proton induced positron emitting radionuclides; these could be measured precisely with positron emission tomography (PET) systems. One main positron emitting radionuclide that could be used for proton range monitoring and verification was found to be 13N that produces a peak close to the Bragg peak. In the present work, we have employed the Monte Carlo method and Spectral Analysis (SA) technique to investigate the feasibility of utilizing the 13N peak for proton range monitoring and verification in inhomogeneous targets. Two different phantom types, namely, (1) ordinary slab and (2) MIRD anthropomorphic phantoms, were used. We have found that the generated 13N peak in such highly inhomogeneous targets (ordinary slab and human phantom) is close to the actual Bragg peak, when irradiated by incident proton beam. The feasibility of using the SA technique to estimate the distribution of positron emitter was also investigated. The current findings and the developed tools in the present work would be helpful in proton range monitoring and verification in realistic clinical radiation therapy using proton beams.