Magnetic Monopoles, as proposed by Dirac, can be used to resolve the quantisation of Electromagnetism, however the problem remains elusive to this day as no experimental evidence for their existence has yet been found. The scope of this thesis is to demonstrate a model of Milli-Magenetically Charged Dark Matter which mixes the visible Abelian Electromagnetic gauge field with the Dark sector. Our formalism involves a velocity- dependent coupling which relativistically depends upon the monopole mass, for which we evaluate the production cross section of proton-proton collisions. Our work focuses on the efforts to observe this particle as part of the MoEDAL-MAPP experiment at the LHC.