A Suffolk County judge has refused a squatter's-rights claim to a 50-foot strip of public land in East Hampton Village made by the heiress to the $18.6 billion Cox media empire.

In a July 1 decision, acting state Supreme Court Justice Ralph Gazzillo rejected Katharine Rayner's claim to a path connecting Georgica Pond to the Atlantic Ocean that beachgoers use to access the water.

Gazzillo, ruling from Riverhead, said the arguments lack any merit because Rayner "constructed improvements on property owned by someone else, to wit: the Village."

The strip, next to the socialite family's 12-acre waterfront compound in East Hampton Village, was donated to the village in 1979 by the descendants of locals Caroline and Walter Keck. But in subsequent years Rayner, 70, and her mother, Anne Cox Chambers, 95, put up a pool heater, fence and pillared gate on the public strip.

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According to court documents, the mother and daughter agreed in 2013 to remove the heater, fence and gate after applying to install a pool.

"The application for the pool was granted, but not for the pool heater to be installed on village property," village attorney Linda Riley said in a telephone interview Thursday. Neither Rayner, who lives in Manhattan, nor her attorneys could be reached for comment.

Riley said that when an inspection was done for the pool project, "We noticed the fence and gates." She said the pool was built but no certificate of occupancy was issued.

Rayner later submitted an application to the zoning board of appeals to build an addition on the house. Riley said the plan was approved with the condition that the fence, gate and pool heater be removed. Rayner, also a member of the New York Public Library Board of Trustees, has applied for a certificate of occupancy for the pool.

"The judge granted our motion to dismiss her action and said basically there was no way she could prove she had squatter's rights over village property," Riley said. "It's municipal property used for public purpose, and the judge agreed."