Jones Wenzl projectors in tensor products of a Verma module and irreducible modules

We construct special idempotents in ${\mathrm{E}\mathrm{n}\mathrm{d}}_{U_q({\mathfrak{s}\mathfrak{l}}_2)}(M(\mu )\otimes V_1^{\otimes n})$ like the Jones Wenzl projector where $M(\mu )$ is Verma module whose highest weight is $\mu$ and $V_1$ is $2$-dimensional irreducible module.