The frustrated magnetism on the Kondo lattice system motivates intriguing Kondo-breakdown beyond traditional Doniach scenario. Among them, fractionalized Fermi liquid (FL*) has drawn a particular interest by virtue of its nature. Here, we study phase diagram $J_{1}$-$J_{2}$ Kondo-Heisenberg model honeycomb at quarter filling. Employing slave-fermion mean-field theory with $d \pm id$ spin ansatz...