In recent years, significant attention has been given to the quantum or nonlinear optical properties of semiconductor quantum dots coupled to plasmonic (metal or metal-dielectric) nanostructures. This happens as the optical properties of quantum dots can be modified, enhanced and efficiently controlled, when placed in the vicinity of plasmonic nanostructures. Among the various quantum optical effects that have been studied in coupled quantum dot – plasmonic nanostructures, particular attention has been given to the modification of the resonance fluorescence spectrum of the quantum dot by the presence of the plasmonic nanostructure, which mainly occurs due to the modification of the spontaneous decay rate of the quantum dot near the plasmonic nanostructure. The most common plasmonic nanostructure that has been studied is the metallic (mainly gold or silver) nanosphere and in most studies the quantum dot is modeled as a two-level quantum system. In this work, we model the quantum dot structure with a three-level V-type quantum system, which can naturally arise in quantum dots, and study the resonance fluorescence spectrum near a metallic nanosphere. We show that the present system leads to quantum interference effects due to the presence of the metallic nanoparticle and specifically due to the anisotropic Purcell effect that occurs in the photon emission of the quantum dot near the metallic nanosphere. We then study the resonance fluorescence spectrum for different distances between the quantum dot and the metallic nanosphere and show that the resonance fluorescence spectrum changes significantly from a single peak spectrum to a multipeak spectrum, an effect that can be explained using a dressed state analysis. The effects of quantum interference in the resonance fluorescence spectrum are also explored.