Siraj Wahhaj, 39, of Clayton County, Ga., was arrested on a Georgia warrant accusing him of abducting his 3-year-old son late last year.
The Sheriff's Office said three women were also detained on Saturday while law enforcement worked to sort out the details of the case.
The sheriff described the conditions at the property as "filthy" and said its residents were poorly clothed, without shoes, and appeared to have had access to a limited food supply, consisting of "a few potatoes and a box of rice".
Morten was charged with harboring a fugitive and Wahhaj was booked without bond on his Georgia warrant for child abduction.
Authorities did not find the 3-year-old, who police believe was kidnapped by Wahhaj, but instead found 11 other children living in squalor, with little food, no water and wearing only rags.
The search at the compound just a few miles from the Colorado border came amid a two-month investigation in collaboration with Clayton County authorities and the FBI, according to Hogrefe. "He's sick, he needs his medications", she said through tears in January.
At that time the father and son were traveling with two adults and five children and told officers they were going to New Mexico for a camping trip, according to police.
A TCSO response team raided the compound on Friday after detectives provided photos of text messages from an unidentified female at the compound pleading for help, money and food.
The toddler, who suffers from seizures, developmental delay, wears braces on his legs, can not walk, and requires daily medication, went to the park in Clayton County with his father in December and never returned. "... We all gave the kids our water and what snacks we had - it was the saddest living conditions and poverty I have seen".
"I absolutely knew that we couldn't wait on another agency to step up and we had to go check this out as soon as possible, so I began working on a search warrant", Hogrefe said in the release.
The authorities had their eye on the compound for two months, but they could not find probable cause to storm the place until they received the message that people were malnourished.
On Thursday, Taos County Sheriff Jerry Hogrefe approved a search warrant for the compound because he believed that a child abduction suspect and the abducted child were at the makeshift residence.
The child and his dad were last seen together on December 13, 2017 when they were in a vehicle that was involved in an accident on I-65 in Alabama. Police said the missing child's father was one of the arrested men.
While the missing 3-year-old boy was not found, police believe he may have been there recently. Three women also found at the property were detained by police but later released.
What originally prompted law enforcement to raid the trailer, the belief that AG Wahhaj was at the compound, turned out to be false, the Sheriff's Office said.
The children, ages 1 to 15, were discovered in the "Third World"-worthy compound, which was built out of garbage, in the desert near Amalia".