The reflectance spectrum, through 1D superconducting photonic bandgap structures organized following the Octonacci sequence, is studied by employing a theoretical calculation based on the transfer-matrix method and the two-fluid Gorter–Casimir theory. The proposed hetero-structures are made up of Yttrium oxide (A) and YBa2Cu3O7 (B) materials. We report the localization of modes for specific generations of the Octonacci sequence and TEM mode. We discuss the field-localization properties for different Octonacci sequences. It is noticed that localized defect modes of intensity scale up to 99% are sensitive to the wave-incident-angle and the TEM wave polarizations. The lateral position of the localized defect mode can be notably adjusted by the operating superconductor’s temperature (T), by applying a structural strain along the stacks, and by specific thicknesses of the used superconductor. The spectra exhibit forbidden wavelength zones around the localized defect modes in which the bandwidths increase with the strain coefficient h and under critical superconductor temperatures. The given structure has potential applications in tunable localized defect modes and is very useful in optical resonators.