The KATRIN experiment aims to determine the absolute neutrino mass by measuring the endpoint region of the tritium $beta$ spectrum. As a large-scale experiment with a sharp energy resolution, high source luminosity and low background it may also be capable of testing certain theories of neutrino interactions beyond the standard model (SM). An example of a non-SM interaction are right-handed currents mediated by right-handed W bosons in the left-right symmetric model (LRSM). In this extension of the SM, an additional SU(2)$_mathrm R$ symmetry in the high-energy limit is introduced, which naturally includes sterile neutrinos and predicts the seesaw mechanism. In tritium $beta$ decay, this leads to an additional term from interference between left- and right-handed interactions, which enhances or suppresses certain regions near the endpoint of the beta spectrum. In this work, the sensitivity of KATRIN to right-handed currents is estimated for the scenario of a light sterile neutrino with a mass of some eV. This has been performed with a Bayesian analysis using Markov Chain Monte Carlo (MCMC). The simulations show that in principle KATRIN is able to set sterile neutrino mass-dependent limits on the interference strength. Thereby, the sensitivity is significantly increased if the $Q$ value of the $beta$ decay can be sufficiently constrained. However, the sensitivity is not high enough to improve current upper limits from right-handed W boson searches at the LHC.
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