Misfit layered compounds, naturally occurring bulk heterostructures, present a compelling alternative to artificially engineered ones, offering a unique platform for exploring correlated phases and quantum phenomena. This study investigates the magnetotransport and superconducting properties of the misfit compound $({\mathrm{PbS})}_{1.13}{\mathrm{TaS}}_2$, comprising alternating PbS and $1H\text{−}{\mathrm{TaS}}_2$ layers. It exhibits distinctive transport properties, including a prominent planar Hall effect and a fourfold oscillatory butterfly-shaped anisotropic magnetoresistance. Moreover, it shows multigap two-dimensional superconductivity with a high in-plane upper critical field, exceeding the Pauli limit. The coexistence of multigap superconductivity and anomalous transport within the same material firmly positions misfit compounds as an ideal platform for realizing quantum effects in the two-dimensional limit of bulk crystals. This opens the door to the development of quantum devices with less complexity and enhanced tunability.

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• Layered crystals
• Single crystal materials
• Transition metal dichalcogenides
• Unconventional superconductors
• Resistivity measurements
• Specific heat measurements