  In this paper, we investigate sign changes of Fourier coefficients of
half-integral weight cusp forms. In a fixed square class $t\mathbb{Z}^2$, we
investigate the sign changes in the $tp^2$-th coefficient as $p$ runs through
the split or inert primes over the ring of integers in a quadratic extension of
the rationals. We show that sign changes occur in both sets of primes when
there exists a prime dividing the discriminant of the field which does not
divide the level of the cusp form and find an explicit condition that
determines whether sign changes occur when every prime dividing the
discriminant also divides the level.
