The true ion-ion interaction governed by the repulsive electrostatic potential and the attractive nuclear potential at small separation is approximated as a Coulomb barrier decorated by an attractive $\delta$-shell potential placed under the barrier. This composite potential can generate unbound or resonance states with positive energy eigen values. The resonances are determined through the calculation of scattering phase-shift $\delta$ of the S-matrix. We make the $\delta$-shell potential complex with an attractive imaginary part in it and obtain the phase-shift $\delta$ as a complex quantity. This complex phase-shift gives non-zero positive reaction cross section to be considered as fusion cross section ${\sigma }_f$ in the calculation. Resonances generated by our model potential combination are clearly manifested as positive peaks in the variation of ${\sigma }_f$ as a function of energy E. The presentation of ${\sigma }_f$ as $\frac{d^2(E{\sigma }_f)}{d{E}^2}$ in variance with E shows oscillations or structures with several peaks and deeps including deeps of negative values. The calculated results of ${\sigma }_f$ and $\frac{d^2(E{\sigma }_f)}{d{E}^2}$ are shown to account for the respective measured results showing oscillatory structures with remarkable success in the fusion data of the ${}^{12}$C+${}^{12}$C, ${}^{12}$C+${}^{16}$O, ${}^{16}$O+${}^{16}$O, and ${}^{40}$Ca+${}^{90,94,96}$Zr systems involving light as well as heavy nuclei. \