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The Public Security Authorities are responsible for maintaining order within the Eldian internment zones such as Liberio on the continental mainland. It includes restricting movement in and out of the ghettos, countering Eldian dissident movements, and sending undesirable Eldians to the island of Paradis where they are turned into mindless Titans.
In the year 830, as of Marley's decision to move against Paradis to secure its vast fossil resource, the PSA were tasked with recruiting warriors from among the Eldian children aged 5 - 7 in service of the Marley government with the promise of designating the families of the chosen children as honorary Marleyans. Zeke Yeager, Bertolt Hoover, Reiner Braun, Annie Leonhart, and Marcel Galliard ended up selected among those children.
Despite its power, the PSA had been actually heavily infiltrated by the Eldian Restoration Movement to the extent that the latter was able to get its hands on censored historical records and important government documents. For example, Eren Kruger, aka "the Owl", was a high-value Eldian agent who managed to become at least on par with Sergeant Major Gross within the PSA command hierarchy. It was not until Zeke Yeager's defection that the PSA was able to weed out most of the conspirators.
PSA personnel is only seen in and around the internment zone, suggesting that it is their sole area of jurisdiction. However, it does share the use of a wharf located in the coast of Paradis with the military, with the PSA uses it for the purpose of exiling undesirable Eldian prisoners into Paradis and the military uses it to dock heavy transport ships.
The PSA turns a blind eye to the brutal behaviors against the Eldians committed by some of its soldiers. For example, PSA member Gross had his sons sadistically kill Faye Yeager by unleashing a pack of dogs upon her for entertainment. The deed did not seem to hurt his career, as by the time of Grisha Yeager's exile to Paradis he had attained, or was still keeping, the rank of Sergeant Major. To crush the Eldian Restoration Movement, the PSA also did not shy from using tortures to obtain confessions from captured dissenters. When he was being interrogated, Grisha had all his fingers cut off by the PSA, one of the many tortures inflicted upon him.
Not everyone in the PSA are brutal, however. For exmaple, in the year 854, there is a duo of PSA guards who are close enough with the warrior cadets that they often make small talks with the Eldian teenagers during their daily passages from the gate. They also know the cadets enough that they are even aware of Falco's affection toward Gabi, and that Falco routinely visits the hospital.
The PSA uniform consists of a soft edge peaked cap with a leather visor, trench coat, a "Sam Browne" style leather belt, a shirt which is worn with a black tie, and a pair of leather jackboots. Its troopers are armed with modern small-arm weaponry such as bolt-action rifles and revolvers.
The Marleyan security force in Kruger and Ymir's time wore a "Napoleonic" style uniform which differs to the modern one by having a kepi, a tunic with two rows of buttons, leather shoulder belts, a waist belt which carries ammo pouches, and a pair of epaulets for higher ranking personnel. The infantry weapons of the time seem to be cap-lock muskets.
Prior to its destruction at the hands of Kruger, the PSA operated at least one steamboat for transportation to the borderline of Paradis where an outpost on the coast of Paradis is located. The outpost is built with a pier by the foot of a 30-meter Wall surrounding a small segment of the coastline.
Although it is unclear when did the Public Security Authorities was founded, the Marleyan persecution of Eldian has been going on long before Grisha's time. At some point between Year 743 and 817, the PSA, or one of its predecessor organizations, crushed a revolutionary army formed by the Eldian royal family staying on the Marleyan mainland.
Eren Kruger's family was burned to death by Marleyan soldiers before his eyes in that event, which made him vowed to restore Eldia into its former glory. When Kruger reached adulthood, he managed to join the PSA by faking the prerequisite blood test with the help of a doctor sympathetic to the Eldian cause. Later, he organized a new resistance group and supplied it with sensitive information from inside the PSA.
At around the same period, the Marleyan security force uncovered an Eldian cult which had Ymir as its figure of worship. She and her fellow cultists were exiled to Paradis where they were converted into Titans.
In 817, PSA sergeant major Gross murdered Faye Yeager, Grisha's sister. The event traumatized Grisha and influenced him to later become the leading figure within the Eldia Restoration Movement.
In 832, the PSA began recruiting Eldian children to be trained as warriors as the Marley government began to move against Paradis for its natural resources. In order to gain control of one of the Titans, Grisha sent Zeke to become one of the recruits, which he succeeded. However, Zeke betrayed the identities of his parents to the Marleyans, allowing the PSA to capture most of the Restorationists.
PSA troopers shipped the prisoners to a borderline outpost in Paradis to be turned into Titans. During the process, Kruger revealed his true identity to Grisha and transformed into the Attack Titan. The ensuing skirmish led to the loss of the entire PSA escort detail and a steamboat.