ALBANY — The state’s new health exchange reports more than 257,000 New Yorkers have completed applications to join and more than 76,000 have enrolled so far in insurance plans or Medicaid.

NY State of Health was established under the federal Affordable Care Act to help extend health coverage to 2.7 million uninsured New Yorkers. Officials say 35,000 enrollments are in the government-funded Medicaid program and 41,000 in one of the plans offered by commercial and nonprofit insurers that chose to participate in the online exchange.

The state exchange, overwhelmed by visitor “hits” the first few days after opening Oct. 1, quadrupled its capacity and has operated the past two months with few reported problems, unlike the related national exchange.

Spikes in usage are expected around the Jan. 1 start of insurance coverage.