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This study explores the new exact solutions of wormhole geometry by imposing the inconsistent Ricci scalar via inhomogeneous spacetime. The current analysis is dealing with the modified f(R, T) theory of gravity. Two different models of gravity that are f1(R) = R − αγtanh(R/γ ) known as exponential gravity model and f1(R) = R − αγ(1-e -R/γ) known as Tsujikawa model, where α, γ are model parameters with matter coupling are considered for the current study. The new feasible solutions for these models by comparing normal and inhomogeneous spacetimes is calculated. Further, we discuss the different properties of the obtained wormhole solutions by taking suitable values of the model parameters analytically and graphically. Moreover, we consider a specific shape functions i.e., b(r) = r0 log( r/r0 + 1) and discuss the energy conditions for both models. The presented wormhole solutions are physically acceptable for the considered exponential and Tsujikawa gravity. [ABSTRACT FROM AUTHOR]