| Summary: | The core of this manuscript is to conduct a broad investigation into the features of static matter configurations with hyperbolical symmetry, which might possibly serve as formation of corresponding spacetime within the limits of f(R,T,Q) gravity, where (Q ≡ R<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mrow><mi>α</mi><mi>σ</mi></mrow></msub></semantics></math></inline-formula>T<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mi>α</mi><mi>σ</mi></mrow></msup></semantics></math></inline-formula>). We recognize that such matter distributions can be anisotropic in pressure, with just two primary stresses unequal and a negative energy density. Usually, negative matter densities are suggested in extreme cosmological and astrophysical situations, particularly with regard to quantum occurrences that might occur within the horizon. Eventually, we construct a generic formalism that allows every static hyperbolically symmetric (<i>HS</i>) fluid solution to be expressed with respect to two generating functions (<i>GFs</i>).
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