  Verlinde has recently conjectured, via a Beckenstein-like thought experiment,
that gravitation, instead of being an elementary force, is an emergent entropic
one. This rather surprising conjecture was actually proved in [Physica A {\bf
505} (2018) 190], in a strictly classical statistical mechanics' environment.
In this Communication, we work in a quantum statistical context to consider the
conjecture in the case of bosons/fermions, in a Tsallis' framework. We prove
that Tsallis' entropy is the operating potential energy in this quantum
treatment, something that does not happen in the case of Boltzmann-Gibbs'
entropy. \color{red} In the classical limit, we show that the emergent force
has a Newtonian dependence with the distance.
