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The motion of a nucleon in q-deformed Eckart potential field coupled with Yukawa-type tensor potential is described by using Dirac equation. The bound state solutions of Dirac equation for q-deformed Eckart potential with Yukawa-type tensor potential under exact spin- and pseudospin-symmetric limit are obtained using finite Romanovski polynomials. The approximate relativistic energy spectra are exactly obtained within the approximation scheme of centrifugal term. The relativistic energy is negative for pseudospin symmetry and positive for spin symmetry. The radial component of Dirac spinors are obtained in terms of Romanovski polynomials under exact spin- and pseudospin-symmetric conditions. The relativistic energy spectrum for the exact spin-symmetric case reduces to non-relativistic energy spectrum in the non-relativistic limit.