  The standard cosmological model, the $\Lambda$CDM model, is the most suitable
description for our universe. This framework can explain the accelerated
expansion phase of the universe but still is not immune to open problems when
it comes to the comparison with observations. One of the most critical issues
is the so-called Hubble constant ($H_0$) tension, namely, the difference of
about $5\sigma$ as an average between the value of $H_0$ estimated locally and
the cosmological value measured from the Last Scattering Surface. The value of
this tension changes from 4 to 6 $\sigma$ according to the data used. The
current analysis explores the $H_0$ tension in the \textit{Pantheon} sample
(PS) of SNe Ia. Through the division of the PS in 3 and 4 bins, the value of
$H_0$ is estimated for each bin and all the values are fitted with a decreasing
function of the redshift ($z$). Remarkably, $H_0$ undergoes a slow decreasing
evolution with $z$, having an evolutionary coefficient compatible with zero up
to $5.8\sigma$. If this trend is not caused by hidden astrophysical biases or
$z$-selection effects, then the $f(R)$ modified theories of gravity represent a
valid model for explaining such a trend.
