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Abstract We explore the shifted $$f(R) (\propto R^{1+\delta })$$ f ( R ) ( ∝ R 1 + δ ) model with $${\delta }$$ δ as a distinguishing physical parameter for the study of constraints at local scales. The corresponding dynamics confronted with different geodesics (null and non-null) along with their conformal analog are investigated. For null geodesics, we discuss the light deflection angle, whereas, for non-null geodesics under the weak field limit, we investigate the perihelion advance of the Mercury orbit in f(R) Schwarzschild background, respectively. The extent of an additional force, appearing for non-null geodesics, depends on $$\delta $$ δ . Such phenomenological investigations allow us to strictly constrain $$\delta $$ δ to be approximately $${\mathcal {O}}(10^{-6})$$ O ( 10 - 6 ) with a difference of unity in orders at galactic and planetary scales and seem to provide a unique f(R) at local scales. Our results suggest that the present form of the model is suitable for the alternative explanation of dark matter-like effects at local scales.