  We investigate the effects of magnetic diffusion on the spectrum of
ultra-high energy cosmic rays (UHECRs) from a cosmological perspective. To this
end, we consider two modified theories of gravity (MTGs), namely, the $f(R)$
gravity and a symmetric teleparallel gravity, also known as $f(Q)$ gravity.
Utilizing these two MTGs, we calculate the suppression in the flux of UHECRs
for a collection of sources. Non-evolution (NE) and cosmic star formation rate
(SFR) scenarios have been considered in our calculation of the suppression
factor. This study also includes a mixed composition scenario involving the
nuclei upto iron (Fe). Furthermore, we provide a parameterization of the
suppression factor for the proton and also for the mixed compositions within
the $f(R)$ and $f(Q)$ theories, considering both NE and SFR scenarios. The
influence of the turbulent magnetic field on the suppression factor is also
incorporated in our work. Comparative analysis of all our results with the
standard $\Lambda$CDM model reveals significant effects of MTGs on the
suppression factor that the $f(R)$ power-law model predicts the lowest
suppression factor, while the $f(Q)$ model predicts the highest, and
interestingly the results from the standard model fall within the range
predicted by these two cosmological models.
