The Allegheny County Executive’s Office expects new federal Medicaid rules taking effect next year to leave roughly 26,000 Allegheny County residents without health coverage, increasing financial pressure on hospitals and the region’s behavioral health system. The changes would hit about 10% of the county’s residents — many of whom remain eligible but could lose benefits because of new paperwork requirements, according to county officials. Of those 26,000 people, county officials said, many remain employed and eligible but will face hurdles with additional administrative barriers. The estimated losses in Allegheny are part of more than 3 million Medicaid recipients expected to lose coverage nationwide, according to the county. County officials estimate that reduced Medicaid enrollment will reduce federal funding for local behavioral health providers by more than $20 million next year in Allegheny County.