The isomeric structure and properties in proton-rich nuclides are crucial for determining the path of the rapid proton capture process ($rp$-process). For example, bound nuclei inside the dripline can have unbound isomeric states and change the $rp$-process pathway. The configuration interaction shell model is used to investigate nuclei around the $Z=N$ line at the southwest region of ${}^{100}\mathrm{Sn}$. The excitation mechanism of $1/2_1^{-}$ isomers is identified as dominated by exciting one nucleon in the $1p_{1/2}$ orbit to the $0g_{9/2}$ orbit. The study explores the decay properties of both the ground and isomeric states. Remarkably, competitive ${\beta }^{+}$ decay and proton emission are predicted in the unbound $1/2_1^{-}$ isomer of ${}^{97}\mathrm{Sn}$, suggesting potential influences on the $rp$-process pathway.

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• Beta decay
• Isomer decays
• Nuclear structure & decays
• Proton emission
• 59 ≤ A ≤ 89
• 90 ≤ A ≤ 149
• Shell model