We investigate proton-rich systems beyond the proton drip line, focusing on the notably poorly known 13F and 15Ne and the yet unobserved 14Ne, whose structure properties remain weakly constrained. Using the Gamow shell model (GSM), which consistently incorporates both inter-nucleon correlations and couplings to the particle continuum, we study oxygen, fluorine, and neon isotopes with mass $A=12-16$. Taking 8C as an inert core, the GSM Hamiltonian based on an effective field theory nucleon-nucleon interaction is optimized for this proton-rich region. The constructed Hamiltonian reproduces the low-lying spectra and decay properties of fluorine and neon isotopes beyond the proton drip line. We quantify many-body configuration and average partial-wave occupancies to elucidate the structural evolution of the drip line nuclei 12–14O, 13–15F, and 14–16Ne. In particular, multi-proton separation energies and spectroscopic factors are analyzed in detail, leading to a prediction for the unresolved ground state of 13F. Furthermore, the candidate 4 p emitter 14Ne is theoretically predicted for the first time, providing valuable guidance for future experimental investigations.