Joseph Adonis was found unresponsive inside a home in Holbrook on Jan. 3.
Police say an 11-year-old was also living in the house at the time.
The 14-month-old was taken to Stony Brook University Hospital where he was pronounced dead.
His parents, Wilkens Adonis and Daryllee Leibrock, both 38 years old, were arraigned Thursday on dozens of charges of drug and weapons possession and child endangerment.
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The Suffolk County district attorney says toxicology tests revealed the baby had cocaine, fentanyl and morphine in his system.
The district attorney said drugs and drug weighing and packaging materials were also found in the home.
Authorities also found a loaded shotgun, rifle and stun gun which were allegedly unsecured and easily accessible to the children.
"Here we are investigating what appears to be an overdose of a baby, and again, this is what we knew was going to happen given the deadly nature of these drugs, and it's going to continue to happen unless we act," Suffolk County District Attorney Ray Tierney said.
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Tierney is asking the New York State Legislature and the governor to provide more help to deal with the fentanyl overdose crisis.
He says there were 399 overdose deaths in Suffolk County in 2022.
Both parents of the child are being held on bail. Bail was set for Leibrock at $250,000 because she allegedly violated an order of protection to stay away from the children and illegal drugs.
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