We have developed a covariant isobar model to phenomenologically explain the four possible isospin channels of Kς photoproduction. To obtain a consistent reaction amplitude, which is free from the lower-spin background problem, we used the consistent electromagnetic and hadronic interactions described in our previous report. We used all available experimental data, including the recent MAMI A2 2018 data obtained for the K0ς+ and K0ς0 isospin channels. By fitting the calculated observables to these data we extract the resonance properties, including their Breit-Wigner and pole parameters. Comparison of the extracted parameters with those listed by the Particle Data Group yields a nice agreement. An extensive comparison of the calculated observables with experimental data is also presented. By using the model we investigated the effects of three different form factors used in the hadronic vertex of each diagram. A brief discussion on the form factors is given.