Isospin of new physics in $|\Delta S|=1$ charmless B decays

New physics (NP) in charmless strangeness-changing $B$ and $B_s$ decays, which are dominated by the $b \to s$ penguin amplitudes, can either preserve isospin or change it by one unit. A general formalism is presented studying pairs of processes related to each other by isospin reflection. We discuss information on $\Delta I$ in NP amplitudes, provided by time-integrated CP-violating rate asymmetries in $B^+$ and $B^0$ decays (or in $B_s$ decays), differences between rates for isospin-reflected processes, and coefficients $S$ of $\sin \Delta m t$ in time-dependent CP asymmetries. These four asymmetries in $B^+$ and $B^0$ decays (or five asymmetries in $B_s$ decays) are shown to determine the magnitude and CP-violating phase of a potential isovector NP amplitude, and the imaginary part of an isoscalar amplitude, assuming that strong phases in NP amplitudes are negligible. This information may be compared with predictions of specific models, for which we discuss a few examples.