In this paper, a study is carried out on the e−p --> e−y*p --> pW−ynu_e production to probe quartic W+W−yy couplings at the Large Hadron electron Collider (LHeC) with s= 1.30, 1.98 TeV and at the Future Circular Collider-hadron electron (FCC-he) with s= 3.46, 5.29 TeV. Production cross-sections are determined for both at leptonic and hadronic decay channels of the W-boson. With the data from future e−p colliders, it is possible to obtain sensitivity measures at 95% C.L
