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In this article, we establish quantitative results for sign changes incertain subsequences of primitive Fourier coefficients of a non-zero Siegelcusp form of arbitrary degree over congruence subgroups. As a corollary of ourresult for degree two Siegel cusp forms, we get sign changes of its diagonalFourier coefficients. In the course of our proofs, we prove the non-vanishingof certain type of Fourier-Jacobi coefficients of a Siegel cusp form and alltheta components of certain Jacobi cusp forms of arbitrary degree overcongruence subgroups, which are also of independent interest.

On sign changes of primitive Fourier coefficients of Siegel cusp forms