We have investigated the survival probability of different charmonium states in a high baryon density parton plasma, expected to be produced in nuclear collisions at the Facility for Antiproton and Ion Research. Charmonia are assumed to undergo complete dissociation by color screening if the in-medium Debye radius becomes comparable to the spatial size of the corresponding bound state. Results indicate a nontrivial dependence of the suppression pattern on the plasma evolution dynamics. A much larger magnitude of suppression is foreseen induced by cold nuclear matter compared to that due to plasma screening. PACS number(s): 25.75.Dw, 25.75.Nq In relativistic nuclear collisions, J /ψ suppression has long been predicted as an unambiguous and experimentally viable signature to indicate the possible occurrence of phase transition to quark-gluon plasma [1]. At the CERN Super Proton Synchrotron (SPS), data on J /ψ suppression were collected for Pb + Pb and In + In collisions, respectively, by the NA50 [2] and NA60 [3] Collaborations at a beam kinetic energy (E b ) of 158 A GeV. Subsequent measurements of charmonium production by the NA60 Collaboration in p + A collisions at the same energy [4], analyzed within the Glauber model framework, suggest that the relative charmonium yield in In + In collisions are in accord within errors with suppression induced by cold nuclear matter (CNM). An anomalous suppression of about 25%-30% still remains visible in the most central Pb + Pb collisions. To date, no measurement exists on charmonium production in heavy ion collisions below the top SPS energy, primarily due to the extremely low production cross sections. The upcoming compressed baryonic matter experiment at the Facility for Antiproton and Ion Research (FAIR) [5] in GSI, Germany, for the first time, is aiming at the measurement of charmonium production in low-energy nuclear collisions, over a range of E b = 10-40 A GeV. In this energy domain, the highest possible baryon densities are expected to be produced at the center of the collision zone [6]. This might lead to a density-driven QCD phase transition of the nuclear matter to a baryon-rich quark-gluon plasma (QGP). In the present Rapid Communication, we plan to estimate the amount of dissociation of the charmonium states induced by color screening inside a hot baryonic plasma. For this purpose, we have developed a variant of the static geometrical threshold model [7]. The Debye screening mass as a function of temperature and baryon chemical potential m D (T , μ B ) in a dynamically evolving plasma is used to decide the fate of different charmonium states implanted in the medium.Quarkonium suppression in nuclear collisions at SPS, the BNL Relativistic Heavy Ion Collider (RHIC), and the CERN Large Hadron Collider has been studied at length in literature [8][9][10][11][12][13][14][15] by using geometrical screening models. Based on semiclassical arguments, they assume some sharply defined resonance formation time and a suppression which is total or * partha.bhaduri@vecc.go...