  Ground-based and space-borne observatories studying exoplanetary transits now
and in the future will considerably increase the number of known exoplanets and
the precision of the measured times of transit minima. Variations in the
transit times can not only be used to infer the presence of additional planets,
but might also provide opportunities for testing new physics in the places
beyond the Solar system. In this work, we take deviation from the
inverse-square law of gravity as an example, focus on the fifth-force-like
Yukawa-type correction to the Newtonian gravitational force which parameterizes
this deviation, investigate its effects on the secular transit timing
variations and analyze their observability in exoplanetary systems. It is found
that the most optimistic values of Yukawa-type secular transit timing
variations are at the level of $\sim 0.1$ seconds per year. Those values
unfortunately appear only in rarely unique cases and, most importantly, they
are still at least two orders of magnitude below the current capabilities of
observations. Such a deviation from the inverse-square law of gravity is likely
too small to detect for the foreseeable future. Meanwhile, systematic
uncertainties, such as the presence of additional and unknown planets, will
likely be exceptionally difficult to remove from a signal that should be seen.
