Standard continuous gravitational-wave searches with pulsar timing arrays (PTAs) neglect cosmological redshift, restricting their applicability to the local Universe. We introduce a redshift-aware PTA framework and apply it to the Parkes PTA Data Release 3, deriving the first direct constraints on supermassive binary black holes (SMBBHs) at the cosmic dawn. Evaluating our limits across a broad redshift range, we observationally establish the non-monotonic mass-redshift exclusion boundary driven by the theoretical “redshift bias”, demonstrating how PTAs can effectively probe sources at extreme distances. Redshift-aware targeted searches toward high-redshift systems, including the ultraluminous quasar J0100+2802 (z = 6.327) and the JWST-discovered galaxy JADES-GS-z14-0 (z = 14.32), rigorously exclude SMBBHs with chirp masses Mc ≳ 10^10 M⊙ across the nanohertz frequency band. Finally, we demonstrate that high-redshift binaries can be robustly detected and localized, allowing for the accurate measurement of their intrinsic properties. Our results provide the tightest constraints to date on SMBBHs at z > 6 and establish a practical framework for probing early-Universe black hole assembly.