  In this paper, we employ one variant of the Generalized Uncertainty Principle
(GUP) model, i.e., the Kempf-Mangano-Mann (KMM) model, and discuss the impact
of GUP on the EoS of nuclear and neutron star matter based on the Relativistic
Mean Field (RMF) model. We input the result in the Serrano-Li\v{s}ka (SL)
gravity theory to discuss the corresponding Neutron Star (NS) properties. We
have shown that the upper bound for the GUP parameter from nuclear matter
properties is $\beta \leq 2\times10^{-7}$ MeV$^{-2}$. If we used this $\beta$
upper bound to calculate NS matter, and considering SL parameter $\tilde{c}$ as
an independent parameter, we have found that the upper bound for the SL
parameter, which modifies the Einstein field equation, is $\tilde{c} \leq 10^7$
m$^2$. This beta upper bound is determined by considering the anisotropy
magnitude smaller than the pressure magnitude. By employing $\beta
=2\times10^{-7}$ MeV$^{-2}$ and $\tilde{c} = 10^7$ m$^2$, we obtain the
mass-radius relation that satisfies NICER data for both PSR J0740+6620 (whose
mass is $\sim 2.1M_\odot$) and PSR J0030+0451 ($M\sim 1.4M_\odot$). Our GUP
parameter upper bound perfectly matches the constraint from $^{87}$Rb
cold-atom-recoil experiment. If we consider that the same strength from the
additional logarithmic term in the entropy from both GUP and SL model are
dependent, for $\beta < 2\times10^{-7}$ MeV$^{-2}$, it is clear that SL
parameter lower bound is $\tilde{c} > -16\times 10^{-34}$ m$^2$. The magnitude
of this bound is $10^{-40}$ smaller than the upper bound magnitude of SL
parameter considering as independent parameter i.e., $\tilde{c} \leq 10^7$
m$^2$.
