We have investigated the spectroscopy of the different exotic tetraquarks such as K, \(f_{0}\) , D, Y, \(Z_{s}\) , \(Z_{c}\) , \(T_{cc}\) , \(T_{cc}\) , \(X_{c}\) etc. embedded in a strongly interacting medium with the variation of density and temperature of the medium. The momentum and density dependent potential and power law type of temperature scaling play crucial roles in this regard. The tetraquarks have been treated as composite system of diquark-antidiquark in the context of Composite Fermion (CF) quasiparticle model and their effective masses have been estimated. Moreover, when these tetraquarks are embedded in a strongly interacting medium, the density and the temperature of the medium affect their masses. These variations of masses have been explored in detail and have been displayed in the graphs. They have also been compared with works of others.