Eighteen sickened Ground Zero workers who missed the deadline for the city’s settlement offer are seeking special permission to join the deal.

Court papers cite “case-specific reasons” why each one failed to sign up before the Jan. 5 deadline.

The Manhattan federal court filing also notes that the “straggling plaintiffs” were always listed among the more than 10,000 Sept. 11 responders eligible for the $662.5 million-plus accord.

In addition to the potential payments to each of the 18, the court papers say letting them join the settlement could add another $2.25 million to the overall amount under terms of incentives built into the deal.

In a statement, the WTC Captive Insurance Co. countered that the plaintiffs had actually “missed several deadlines since the June announcement of a revised agreement.”

“These plaintiffs can instead choose to apply to the reopened Victim Compensation Fund, under the James Zadroga Health and Compensation Act,” the statement said.