A search for charged-lepton-flavor violating Formula Presented (Formula Presented, Formula Presented) interactions is presented, considering both top-quark production and decay. The data analyzed correspond to Formula Presented of proton-proton collisions at a center-of-mass energy of Formula Presented recorded with the ATLAS detector at the Large Hadron Collider. The analysis targets events containing two muons with the same electric charge, a hadronically decaying Formula Presented-lepton and at least one jet, with exactly one Formula Presented-tagged jet, produced by a Formula Presented interaction. Agreement with the Standard Model expectation within 1.6 standard deviations is observed, and limits are set at the 95% confidence level (CL) on the charged-lepton-flavor violation branching ratio of Formula Presented. An effective field theory interpretation is performed yielding 95% CL limits on Wilson coefficients, dependent on the flavor of the associated light quark and the Lorentz structure of the coupling. These range from Formula Presented for Formula Presented to Formula Presented for Formula Presented. An additional interpretation is performed for scalar leptoquark production inducing charged-lepton-flavor violation, with fixed intergenerational couplings. Upper limits on leptoquark coupling strengths are set at the 95% CL, ranging from Formula Presented to Formula Presented for leptoquark masses between 0.5 and 2.0 TeV.