We have studied the Zero-Bias Conductance Peak (ZBCP) of the tunneling conductance measured on (1,1,0)-oriented Y1-yCayBa2Cu3O7-x thin films as a function of doping and of magnetic field. A spontaneous (zero field) split of the ZBCP was observed only in overdoped samples (either by O or by Ca). The magnitude of this split was found to be linear in doping. All samples exhibited a magnetic-field splitting, also strongly doping dependent. The field susceptibility χ = dδ/dH|H → 0 diverges at the point at which spontaneous ZBCP splitting occurs, its inverse value, χ-1, following a linear doping dependence on both the underdoped and overdoped sides. We discuss these results in terms of recent theoretical models of Time Reversal Symmetry Breaking (TRSB).