To obtain analytically relativistic quintessence anisotropic spherical solutions in the f(T) paradigm is the primary objective of this paper. To do this, the pressure anisotropy condition is imposed, and we employ a metric potential of the Tolman–Kuchowicz (TK) type. We also suppose that our current model incorporates a quintessence field characterized by a parameter ω q , in addition to the anisotropic matter distribution. In the presence of the parameter α, the field equations are modified by the choice of the f(T) function. The f(T) gravity parameter α adds new components to the basic physical characteristics, such as density, pressure, subliminal sound velocity, surface redshift, etc, of the present model. By selecting the compact star Her X-1 and varying α from 0.5 to 2.5, we examined all the physical characteristics of the model parameter of the configuration. The graphical process demonstrates that a more compact item is produced with greater values of α. The hydrostatic equilibrium condition of the model is discussed, as well as the mass-radius relationship for our current model is obtained.