Phenomenology of nonstandard<b><i>Z</i></b>couplings in exclusive semileptonic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>b</mml:mi></mml:mrow><mml:mrow><mml:mo>→</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:mrow><mml:mi>s</mml:mi></mml:math>transitions

The rare decays $\stackrel{\ensuremath{\rightarrow}}{B}{K}^{(*)}{l}^{+}{l}^{\ensuremath{-}},$ $\stackrel{\ensuremath{\rightarrow}}{B}{K}^{(*)}\ensuremath{\nu}\overline{\ensuremath{\nu}}$ and ${B}_{s}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ are analyzed in a generic scenario where new physics effects enter predominantly via Z penguin contributions. We show that this possibility is well motivated on theoretical grounds, as the $\overline{s}\mathrm{bZ}$ vertex is particularly susceptible to nonstandard dynamics. In addition, such a framework is also interesting phenomenologically since the $\overline{s}\mathrm{bZ}$ coupling is rather poorly constrained by present data. The characteristic features of this scenario for the relevant decay rates and distributions are investigated. We emphasize that both sign and magnitude of the forward-backward asymmetry of the decay leptons in $\overline{B}\ensuremath{\rightarrow}{K}^{*}{l}^{+}{l}^{\ensuremath{-}},$ ${\mathcal{A}}_{\mathrm{FB}}^{(\overline{B})},$ carry sensitive information on new physics. The observable ${\mathcal{A}}_{\mathrm{FB}}^{(\overline{B})}+{\mathcal{A}}_{\mathrm{FB}}^{(B)}$ is proposed as a useful probe of nonstandard $\mathrm{CP}$ violation in $\overline{s}\mathrm{bZ}$ couplings.