Resonant excitation of quantum emitters has thus far focused on developing optimal single-photon sources. However, the finding of more general quantum states of light remains scarce. Here, we demonstrate the on-demand generation of coherent superpositions of photon Fock-states. We show that resonantly exciting a semiconductor quantum dot produces non-classical light in superpositions of photon-numbers along the Rabi cycles. Driving the atomic system up to full atomic inversion results in quantum superpositions of ground and excited atomic states, which, via spontaneous emission, leads to superpositions of vacuum and a single-photon, with their relative populations controlled by the driving laser intensity. Moreover, we show that driving the system with stronger pulses beyond full-inversion results in a coherent superposition of vacuum, one, and two photons, where the two-photon term exceeds the single-photon component; a state incidentally resembling a small Schrödinger-cat state. New paths for optical quantum technologies with access to the photon-number degree-of-freedom may now be accessible.