A construction of cyclic ferocious extensions by the Inaba equation is presented. It gives a partial answer to the question about construction of cyclic extensions with small ramification depth. The construction is based on a method similar to that used by I. B. Zhukov and E. F. Lysenko (2017), and gives a tower of simple extensions with suitable ramification jumps. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.