We discuss the \(p\bar{p}\) annihilation into a pair of charmed \(D\) mesons not far from the threshold of the reaction. An interesting interference pattern in the differential cross section is predicted to arise from the existence of both \(t\)-channel charmed-baryon exchange and \(s\)-channel \(\Psi^{''}\) charmonium resonance amplitudes. We argue that the experimental study of this process would provide new and valuable information about the unknown \(p\bar{p}\Psi^{''}\) and \(\Lambda_c N D\) couplings. These are important to know to solve the long-standing puzzle of the heavy flavour contents of baryons and to test the semi-local duality.