Much of the debate over Republican efforts to roll back the Affordable Care Act has focused on the impact cuts would have on working-age adults, millions of whom gained coverage under the healthcare law that President Obama signed in 2010. But in Fayette County and 779 other mostly rural counties across the country — the vast majority of which went for Trump — more than half the children rely for coverage on Medicaid and the related Children’s Health Insurance Program, or CHIP, according to a Times analysis of county voting data, census data and Medicaid enrollment data.