  The (2+1)-dimensional static magnetic susceptibility in strong-coupling is
studied via a Reissner-Nordstr\"{o}m-AdS geometry. The analyticity of the
susceptibility on the complex momentum $\mathfrak{q}$-plane in relation to the
Friedel-like oscillation in coordinate space is explored. In contrast to the
branch-cuts crossing the real momentum-axis for a Fermi liquid, we prove that
the holographic magnetic susceptibility remains an analytic function of the
complex momentum around the real axis in the limit of zero temperature, At zero
temperature, we located analytically two pairs of branch-cuts that are parallel
to the imaginary momentum-axis for large $|\text{Im}\ \mathfrak{q}|$ but become
warped with the end-points keeping away from the real and imaginary
momentum-axes. We conclude that these branch-cuts give rise to the exponential
decay behaviour of Friedel-like oscillation of magnetic susceptibility in
coordinate space. We also derived the analytical forms of the susceptibility in
large and small-momentum, respectively.
