  In this work we present a keV-scale sterile-neutrino search with the first
tritium data of the KATRIN experiment, acquired in the commissioning run in
2018. KATRIN performs a spectroscopic measurement of the tritium $\beta$-decay
spectrum with the main goal of directly determining the effective electron
anti-neutrino mass. During this commissioning phase a lower tritium activity
facilitated the search for sterile neutrinos with a mass of up to $1.6\,
\mathrm{keV}$. We do not find a signal and set an exclusion limit on the
sterile-to-active mixing amplitude of down to $\sin^2\theta < 5\cdot10^{-4}$
($95\,\%$ C.L.), improving current laboratory-based bounds in the
sterile-neutrino mass range between 0.1 and $1.0\, \mathrm{keV}$.
