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The observation of time-reversal symmetry breaking and large residual density of states in tetragonal ${\mathrm{FeSe}}_{1-x}{\mathrm{S}}_x$ suggests a novel type of ultranodal superconducting state with Bogoliubov Fermi surfaces (BFSs). Although such BFSs in centrosymmetric superconductors are expected to be topologically protected, the impurity effect of this exotic superconducting state remains elusive experimentally. Here, we investigate the impact of controlled defects introduced by electron irradiation on the superconducting state of tetragonal ${\mathrm{FeSe}}_{1-x}{\mathrm{S}}_x$ ($0.18\le x\le 0.25$). The temperature dependence of magnetic penetration depth is initially consistent with a model with BFSs in the pristine sample. After irradiation, we observe a nonmonotonic evolution of low-energy excitations with impurity concentrations. This nonmonotonic change indicates a transition from nodal to nodeless, culminating in gapless with Andreev bound states, reminiscent of the nodal $s_{\pm }$ case. This points to the accidental nature of the possible BFSs in tetragonal ${\mathrm{FeSe}}_{1-x}{\mathrm{S}}_x$, which are susceptible to disruption by the disorder.

The kagome metal ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ exhibits an unusual charge-density-wave (CDW) order, where the emergence of loop current order that breaks time-reversal symmetry (TRS) has been proposed. A key feature of this CDW phase is a nonmonotonic Hall effect at low fields, often attributed to TRS breaking. However, its origin remains unclear. Here, we conduct comprehensive magnetotransport measurements on ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ and, through mobility spectrum analysis, identify the formation of tiny Fermi pockets with extremely high mobility below the CDW transition. Furthermore, electron irradiation experiments reveal that the nonmonotonic Hall effect is significantly suppressed in samples with reduced mobility, despite no substantial change in the electronic structure. These results indicate that the nonmonotonic Hall effect originates from these tiny Fermi pockets with high mobility carriers rather than anomalous Hall mechanisms, providing new insights into understanding the Hall anomaly in this kagome system.