[en] The neutron-rich dysprosium isotopes ¹⁶⁸Dy₁₀₂ and ¹⁶⁹Dy₁₀₃ have been investigated using the EURICA γ-ray spectrometer, following production via in-flight fission of a high-intensity uranium beam in conjunction with isotope separation through the BigRIPS separator at RIBF in RIKEN Nishina Center. For ¹⁶⁸Dy, a previously unreported isomer with a half-life of 0.57(7) μs has been identified at an excitation energy of 1378 keV, and its presence affirmed independently using γ-γ-γ coincidence data taken with Gammasphere via two-proton transfer from an enriched ¹⁷⁰Er target performed at Argonne National Laboratory. This isomer is assigned J^π = K^π = (4¯) based on the measured transition strengths, decay patterns, and the energy systematics for two-quasiparticle states in N = 102 isotones. The underlying mechanism of two-quasiparticle excitations in the doubly midshell region is discussed in comparison with the deformed QRPA and multi-quasiparticle calculations. In ¹⁶⁹Dy, the B(E2) value for the transition de-exciting the previously unreported K^π = (1/2¯) isomeric state at 166 keV to the K^π = (1/2¯) ground state is approximately two orders of magnitude larger than the E2 strength for the corresponding isomeric-decay transition in the N = 103 isotone ¹⁷³Yb, suggesting the presence of a significant γ-vibrational admixture with a dominant neutron one-quasiparticle component in the isomeric state.