The video was released by U.S Border Patrol Raul Ortiz on Twitter Monday, but authorities say the incident happened on May 15.
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It shows an unknown person lowering the child before dropping them from the barrier. A second person is dropped moments later.
Portions of the video show the child waiting as the person directed him or her to stand aside.
Ortiz said agents treated the child at the scene and is expected to be OK. He said agents also reported hearing gunshots while helping the child.
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The incident remains under investigation.