A search for pair produced scalar fermions with couplings that violate $R$-parity has been performed using data samples corresponding to an integrated luminosity of about 700~pb$^{-1}$ collected with the OPAL detector at LEP above the ${\mathrm Z}^{0}$ peak, at centre-of-mass energies up to $\sqrt{s}=$ 209~GeV. An important consequence of $R$-parity breaking interactions is that the lightest supersymmetric particle is expected to be unstable. Searches for $R$-parity violating decays of charged sleptons, sneutrinos and stop quarks have been performed under the assumptions that the lightest supersymmetric particle decays promptly and that only one of the $R$-parity violating couplings is dominant for each of the decay modes considered. Such processes would yield multi-leptons, jets plus leptons or multi-jets, with or without missing energy, in the final state. No significant excess of such events has been observed. Limits on the production cross-sections of scalar fermions in $R$-parity violating scenarios are obtained. Mass exclusion regions are also presented in the framework of the Constrained Minimal Supersymmetric Standard Model.