Verizon Communications Inc.’s Oath will pay $4.95 million to settle New York state claims that it failed to protect kids’ online privacy through its advertising business.

AOL, which Oath owns, helped place targeted display ads on hundreds of websites it knew were directed to children under the age of 13, according to the New York Attorney General’s office.

The company collected and disclosed personal data on children through auctions for ad space, allowing businesses to serve targeted ads to kids—a...