  Modeled searches of gravitational wave signals from compact binary mergers
rely on template waveforms determined by the theory of general relativity (GR).
Once a signal is detected, one generally performs the model agnostic test of
GR, either looking for consistency between the GR waveform and data or
introducing phenomenological deviations to detect the departure from GR. The
non-trivial presence of beyond-GR physics can alter the waveform and could be
missed by the GR template-based searches. A recent study [Phys. Rev. D 107,
024017 (2023)] targeted the binary black hole merger, assuming the parametrized
deviation in lower post-Newtonian terms and demonstrated a mild effect on the
search sensitivity. Surprisingly, for the search space of binary neutron star
(BNS) systems where component masses range from 1 to $2.4\:\rm{M}_\odot$ and
parametrized deviations span $1\sigma$ width of the deviation parameters
measured from the GW170817 event, the GR template bank is highly ineffectual
for detecting the non-GR signals. Here, we present a new hybrid method to
construct a non-GR template bank for the BNS search space. The hybrid method
uses the geometric approach of three-dimensional lattice placement to cover
most of the parameter space volume, followed by the random method to cover the
boundary regions of parameter space. We find that the non-GR bank size is
$\sim$15 times larger than the conventional GR bank and is effectual towards
detecting non-GR signals in the target search space.
