Scanning tunneling spectroscopy was performed on (110)-oriented thin films of Ca-overdoped Y$_{0.95}$Ca$_{0.05}$Ba$_2$Cu$_3$O$_{7-delta}$ at 4.2K, to probe the local evolution of Andreev$-$Saint-James surface states in a c-axis magnetic field. In zero field, we observed conductance spectra with spontaneously-split peaks and spectra with unsplit zero-bias peaks. The former showed enhanced splitting with field, and the latter showed threshold splitting above finite fields. Although both field evolutions can be described in terms of screening and orbital supercurrents, within the framework of $dpm ialpha$ pairing ($d$=$d_{x^2-y^2}$; $alpha$=$d_{xy}$,$s$), the enhanced splitting is consistent with only the $d$ + $ialpha$ state. Our results have direct implications on the stability of broken time-reversal symmetry in cuprate superconductors.
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