Highly charged nickel ions have been suggested as candidates for the ultra-precise optical clock, meanwhile the relevant experiment has been carried out. In the framework of the multiconfiguration Dirac-Hartree-Fock (MCDHF)method, we calculated the hyperfine interaction constants, the Landé g-factors, and the electric quadrupole moments for the low-lying states in the 61Ni11+, 61Ni12+, 61Ni14+, and 61Ni15+ions. These states are clock states of the selected clock transitions in highly charged nickel ions (see Fig. 1). Based on discussing the effects of the electron correlations, the Breit interaction, and quantum electrodynamics (QED) effect on these physical quantities, reasonable uncertainties were obtained for our calculated results. In addition, the electric quadrupole frequency shifts and the Zeeman frequency shifts of the clock transitions concerned were analyzed.