This baby’s not on board with ObamaCare.

Long Islander Cornelius Kelly found it would be no problem to secure a family plan for his wife and three older kids through New York’s health-care exchange, but his 18-month-old daughter was out in the cold. The baby would need her own insurance policy.

“I couldn’t believe what I was being told,” said the dad from East Quogue, in Suffolk.

Kelly said he was no fan of the Affordable Care Act, but when he received notice a few weeks ago that his current insurance plan was being canceled, he tried the New York State of Health Web site.

Kelly, 41, and his wife, Jennifer, 42, are self-employed and have always had to buy their own insurance. Kelly runs a title insurance business in Westhampton, and his wife is a pediatrician in private practice in Miller Place. “I initially went on with a lot of optimism,” he said.

Kelly said none of the plans offered out-of-network coverage, which was something he wanted. But even worse, they only covered his three older children, who are 3, 5 and 6.

When Kelly called a representative, he was told his daughter had to be 2 before she could be covered under a family plan. He would have to buy a separate plan for her, at monthly premiums that ranged between $117.21 and $369.31. The cost would be on top of a family plan with premiums ranging from $810.84 to $2,554.71 a month.

Kelly said he had been paying about $1,000 a month.

Unwilling to put his daughter on a separate policy, Kelly found a family plan in the private marketplace for about $1,250 a month.

It was only after The Post called the state Health Department that Kelly said he got a call from a department representative telling him it had all been a mistake, and the baby could be covered after all under a family plan.

The department would not comment on the specifics of Kelly’s situation or why it told the family three times that the baby wasn’t covered. It would only say, “All children in the family are covered under a family policy. A separate policy is not needed for the 1 1/2 year old child.”