Within the framework of the Lanzhou quantum molecular dynamics model, the deep subthreshold antiproton production in heavy-ion collisions has been investigated thoroughly. The elastic scattering, annihilation and charge exchange reactions associated with antiproton channels are implemented in the model. The attractive antiproton potential extracted from the G-parity transformation of nucleon selfenergies reduces the threshold energies in meson-baryon and baryon-baryon collisions, and consequently enhances the antiproton yields to some extent. The calculated invariant spectra are consistent with the available experimental data. The primordial antiproton yields increase with the mass number of the colliding system. However, annihilation reactions reduce the antiproton production which becomes independent of the colliding partners. Anti-flow phenomena of antiprotons correlated with the mean field potential and annihilation mechanism is found by comparing them with the proton flows. Possible experiments at the high-intensity heavy-ion accelerator facility (HIAF) in China are discussed.