  In this paper, we establish the Cowling--Price's, Hardy's and Morgan's
uncertainty principles for the Opdam-Cherednik transform on modulation spaces
associated with this transform. The proofs of the theorems are based on the
properties of the heat kernel associated with the Jacobi-Cherednik operator and
the versions of the Phragm{\'e}n-Lindl{\"o}f type result for the modulation
spaces.
