  The aim of this paper is to establish a few qualitative uncertainty
principles for the windowed Opdam-Cherednik transform on weighted modulation
spaces associated with this transform. In particular, we obtain the
Cowling-Price's, Hardy's and Morgan's uncertainty principles for this transform
on weighted modulation spaces. The proofs of the results are based on versions
of the Phragm{\'e}n-Lindl{\"o}f type result for several complex variables on
weighted modulation spaces and the properties of the Gaussian kernel associated
with the Jacobi-Cherednik operator.
