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In the present investigation, compact stellar models are dealt with in the framework of the modified gravity theory, specifically of f(𝕋,𝒯) type. We have considered that the compact objects are following a spherically symmetric static metric and obtained the Einstein field equations in the spacetime of f(𝕋,𝒯). To make the Einstein equations solvable, we employ the methodology of conformal Killing vectors. Thereafter by using the MIT bag equation of state to the compact stars, considering that the stars are formed by strange quark, we find the solutions set. The solutions are examined via several physical testings which exhibit viability of the model.