The frustrated magnetism on the Kondo lattice system motivates intriguing Kondo breakdown beyond the traditional Doniach scenario. Among them, the fractionalized Fermi liquid (FL*) has drawn particular interest by virtue of its fractionalized nature. Here we study the phase diagram of the J(1)-J(2) Kondo-Heisenberg model on a honeycomb lattice at a quarter filling. Employing the slave-fermion mean-field theory with d +/- id spin liquid ansatz and exact diagonalization, we discuss the emergence of partial Kondo screening in the frustrated regime with comparable J(1) and J(2), and the fractionalized superconductor (SC*), which is a superconductor analogy of the FL*. Due to the larger number of local spin moments than itinerant electrons, the magnetic fluctuation is still significant even in the strong-coupling limit, which influences the thermodynamic and transport properties qualitatively. In particular, we estimate the thermal conductance to probe the low-energy excitation and show the anomalous behavior in the SC* phase in contrast to the conventional superconductors.