  In this article, we establish quantitative results for sign changes in
certain subsequences of primitive Fourier coefficients of a non-zero Siegel
cusp form of arbitrary degree over congruence subgroups. As a corollary of our
result for degree two Siegel cusp forms, we get sign changes of its diagonal
Fourier coefficients. In the course of our proofs, we prove the non-vanishing
of certain type of Fourier-Jacobi coefficients of a Siegel cusp form and all
theta components of certain Jacobi cusp forms of arbitrary degree over
congruence subgroups, which are also of independent interest.
