  It is known that using Boltzmann-Gibbs statistics, Bekenstein-Hawking entropy
$S_{HB}$, and the quasinormal modes of black holes, one finds that the lowest
value of spin is $j_{min}=1$. In this paper, we determine $j_{min}$, using
non-extensive entropies that depend only on the probability (known as Obregon's
entropies and have been derived from superstatistics). We also calculate
$j_{min}$ for a set of non-extensive entropies that have free parameters and
are written in terms of $S_{BH}$. We find that $j_{min}$ depends on the area
and the non-extensive parameter.
  For the non-extensive entropies that only depend on the probability, we find
that the modification is only present for micro black holes. For classical
black holes the results are the same as for the Boltzmann-Gibbs statistics.
