Background: The Z=50 shell closure, near N=82, is unique in the sense that it is the only shell closure with the spin-orbit partner orbitals, πg9/2 and πg7/2, enclosing the magic gap. The interaction of the proton hole/particle in the above-mentioned orbitals with neutrons in the νh11/2 orbital is an important prerequisite to the understanding of the nuclear structure near N=82 and the νπ interaction. Purpose: To explore the structural similarity between the high-spin isomeric states in In (Z=49), Sn (Z=50), and Sb (Z=51) isotopes from a microscopic point of view. In addition, to understand the role of a proton hole or particle in the spin-orbit partner orbitals, πg9/2 and πg7/2, respectively, with neutron holes in the νh11/2 orbital on these aforementioned isomers. Methods: The fusion and transfer induced fission reaction Be9(U238, f) with 6.2 MeV/u beam energy, using a unique setup consisting of AGATA, VAMOS++, and EXOGAM detectors, was used to populate through the fission process and study the neutron-rich In119,121 isotopes. This setup enabled the prompt-delayed γ-ray spectroscopy of isotopes in the time range of 100ns-200μs. Results: In the odd-AIn119,121 isotopes, indications of a short half-life 19/2- isomeric state, in addition to the previously known 25/2+ isomeric state, were observed from the present data. Further, new prompt transitions above the 25/2+ isomer in In121 were identified along with reevaluation of its half-life. Conclusions: The experimental data were compared with the theoretical results obtained in the framework of large-scale shell-model calculations in a restricted model space. The (πg9/2νh11/2;I|Ĥ|πg9/2νh11/2;I) two-body matrix elements of residual interaction were modified to explain the excitation energies and the B(E2) transition probabilities in the neutron-rich In isotopes. The (i) decreasing trend of E(29/2+)-E(25/2+) in odd-In (with dominant configuration πg9/2-1νh11/2-2 and maximum aligned spin of 29/2+) and (ii) increasing trend of E(27/2+)-E(23/2+) in odd-Sb (with dominant configuration πg7/2+1νh11/2-2 and maximum aligned spin of 27/2+) with increasing neutron number could be understood as a consequence of hole-hole and particle-hole interactions, respectively.