Engineering sequence-specific antibodies (Abs) against phosphotyrosine (pY) motifs embedded in folded polypeptides remains highly challenging because of the stringent requirement for simultaneous recognition of the pY motif and the surrounding folded protein epitope. Here, we present a method named phosphotyrosine Targeting by Recombinant Ab Pair, or pY-TRAP, for in vitro engineering of binders for native pY proteins. Specifically, we create the pY protein by unnatural amino acid misincorporation, mutagenize a universal pY-binding Ab to create a first binder B1 for the pY motif on the pY protein, and then select against the B1-pY protein complex for a second binder B2 that recognizes the composite epitope of B1 and the pY-containing protein complex. We applied pY-TRAP to create highly specific binders to folded Ub-pY59, a rarely studied Ub phosphoform exclusively observed in cancerous tissues, and ZAP70-pY248, a kinase phosphoform regulated in feedback signaling pathways in T cells. The pY-TRAPs do not have detectable binding to wild-type proteins or to other pY peptides or proteins tested. This pY-TRAP approach serves as a generalizable method for engineering sequence-specific Ab binders to native pY proteins.