X-ray-bright knots of kiloparsec-scale jets of several radio-loud quasars are an actively discussed issue. Among various models for explaining observations of these phenomena, synchrotron radiation from the electron population that differs from radio to IR-emitting electrons, is promising. However, the origin of this electron population has been debated. Recently, we proposed that this electron population is produced by proton-photon collisions (mainly, the Bethe-Heitler process), and we applied this model to PKS 0637-752. We found that this model works if the proton power is an order of magnitude larger than the Eddington power. In this paper we apply this model to the X-ray emission in the knots of 3C 273 and PKS 1136-135. The target photons for electron-positron pair production are supplied by synchrotron radiation at the radio-IR by primary electrons and by the active galactic nucleus (AGN) core, as well as cosmic microwave background (CMB) radiation. The effects of the AGN photons are included for the first time in the hadronic model. Though the observed X-ray flux is obtained with the contribution of the AGN photons, the required proton power turns out to be highly super-Eddington. However, we find that our model works for a nearly Eddington proton power, if the photon density of the AGN is enhanced. This can occur if the AGN photons are more beamed toward the X-ray knots than toward our line of sight and the AGN photon frequency is shifted by the Doppler effect.