Abstract In this article we confront a class of f ( Q ) gravity models with observational data of galaxy–galaxy lensing. Specifically, we consider f ( Q ) gravity models containing a small quadratic correction when compared with general relativity (GR), and quantify this correction by a model parameter, α . To derive the observational constraints, we start by extracting spherically symmetric solutions, which correspond to deviations from the Schwarzschild solution that depends on the model parameters in a twofold way, i.e., a renormalized mass and a new term proportional to r −2 . Then, we calculate the effective lensing potential, the deflection angle, the shear component, and the effective excess surface density profile. After that, we employ a group catalog and a shape catalog from the Sloan Digital Sky Survey Data Release 7 for the lens and source samples, respectively. Moreover, we handle the off-center radius as a free parameter and constrain it using a Markov Chain Monte Carlo method. Concerning the deviation parameter from GR we derive α = 1.202 − 0.179 + 0.277 × 10 − 6 Mpc − 2 at the 1 σ confidence level, and then compare the fitting efficiency with the standard Λ cold dark matter paradigm by applying the Akaike information criterion and Bayesian information criterion. Our results indicate that the f ( Q ) corrections alongside the off-center effect yield a scenario that is slightly favored.

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