A bill to amend the Immigration and Nationality Act to provide for an electronic employment verification system, and for other purposes.

E-Verify System Act of 2018 This bill (1) directs the Department of Homeland Security to develop an electronic employment eligibility verification system modeled after E-Verify and phases in the mandatory use of such a system, (2) directs the Social Security Administration to begin work toward the issuance of fraud-resistant and tamper-resistant Social Security cards, and (3) establishes the Office of the Small Business and Employee Advocate to assist small businesses and individuals to comply with employment-related immigration laws.