Description: Matching current observations on non-baryonic Dark Matter (DM), Cantor Dust was recently conjectured to emerge as large-scale topological structure formed in the early stages of cosmological evolution. The mechanism underlying the formation of Cantor Dust hinges on dimensional condensation of spacetime endowed with minimal fractality. It is known that anyons are quasiparticles exhibiting anomalous statistics and fractional charges in 2+1 spacetime. This brief report is a preliminary exploration of the intriguing analogy between anyons and the Cantor Dust picture of DM.