  In this work we consider lightcone fluctuation effects in a five-dimensional
spacetime arising as a consequence of the compactification of the extra
dimension via a quasiperiodic condition, characterized by a phase angle
$2\pi\alpha$. By considering light propagating in a non-compactified direction
we are able to compute both the renormalized graviton two-point function and
the flight time of a photon caused by the fluctuations. We show that the
resulting expressions depend on the quasiperiodic parameter, the
compactification length and also on the distance traveled by the photon. Based
on the Near-Infrared Spectrograph (NIRSpec) sensitivity built on the James Webb
Space Telescope, we discuss the possibility of making estimations on the size
of the extra dimension if one assumes that the mean deviation on the flight
time of photons can be observed through the NIRSpec. We also analyze the
differences between the estimations in the periodic $\alpha=0$, antiperiodic
$\alpha=1/2$ and other condition cases for $\alpha$.
