Bifurcation and quasiperiodic behaviors of ion acoustic waves in electron-ion magnetoplasmas with non- thermal electrons featuring Cairns-Tsallis distribution have been investigated on the frameworks of non-perturbed and perturbed Kadomtsev-Petviashvili (KP) equations, respec- tively. Employing the reductive perturbation technique (RPT), we have derived the KP equation in electron- ion magnetoplasmas with nonthermal electrons featur- ing Cairns-Tsallis distribution. Bifurcations of ion acous- tic traveling waves of the KP equation have been pre- sented. Using the bifurcation theory of planar dynam- ical systems, the existence of solitary wave solutions and periodic traveling wave solutions has been estab- lished. Three analytical solutions of these waves have been derived depending on the system parameters. Considering an external periodic perturbation, we have presented the quasiperiodic behavior of ion acoustic waves in electron-ion magnetoplasmas.