The Standard Model (SM) of particle physics, having been confirmed by numerous experiments, is one of the most successful theories in physics. It describes all known elementary particles and their interactions through the electromagnetic, strong and weak force. The SM can be studied by colliding particles at high energies using particle accelerators, such at the LHC at CERN. Despite its success, there are several observed phenomena that indicate that there is new physics beyond the SM. One approach to search for new phyics is using the Effective Field Theory (EFT) framework, which parameterizes how new physics at higher energies alters existing couplings or adds new couplings to the SM particles. One promising process that can probe for new physics is the production of a top-antitop quark pair ( tt ) in association with a W boson and an extra jet ( j ), where the W boson scatters off of one of the top quarks via the electroweak interaction (EW). This thesis describes the first cross section measurement for this process, denoted ( ttWj ) EW , as well as parametrizes the cross section in the EFT framework in terms of the EFT coefficient C φt . An auxiliary measurement of the ttW cross section is also performed and presented. The analysis uses head-on proton-proton collisions at a center-of-mass energy of √ s = 13 TeV recorded by the ATLAS experiment. The data correspond to an integrated luminosity of 139 fb -1 , collected during the period from 2015 to 2018. The data are filtered for final states with two electrons or muons and at least four jets, out of which at least one should originate from a b hadron. The ttW cross section is found to be σ ttW = 0.74 +0.15 -0.14 pb, which is consistent with previous measurements. Using blinded data, an expected upper limit on the cross section (defined for jets with transverse momenta of at least 20 GeV/ c ), as well as an expected 95% CL limit on the C φt coefficient, are obtained as σ ( ttWj)EW < 0.21 pb and -11.1 < C φt < 10.2, respectively.