The $beta$ decay of the isomeric and ground state of $^{50}$Sc to the semi-magic nucleus $^{50}_{22}$Ti$_{28}$ has been studied using a $^{50}$Ca beam delivered to the GRIFFIN $gamma$-ray spectrometer at the TRIUMF-ISAC facility. $beta$-decay branching ratios are reported to 16 excited states with a total of 38 $gamma$-ray transitions linking them. These new data significantly expands the information available over previous studies. Relative intensities are measured to less than 0.001$%$ that of the strongest transition with the majority of $gamma$-ray transitions observed here in $beta$ decay for the first time. The data are compared to shell-model calculations utilizing both phenomenologically-derived interactions employed in the ${it pf}$ shell as well as a state-of-the-art, ${it ab~initio}$ based interaction built in the valence-space in-medium similarity renormalization group framework.
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