The shot was fired on Thursday, October 26 outside the Harbor House apartments in Claymont.
Investigators say the apartment was occupied by a 63-year-old woman at the time.
The 15-year-old was developed as a suspect during the investigation, and he was arrested on Thursday.
A search warrant on his Denham Avenue home revealed a .32 caliber handgun, police say. He was taken into custody without incident.
The teen has been charged with felony reckless endangering, possession of a firearm during the commission of a felony and possession of a firearm by prohibited juvenile.
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