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The Public Security Authorities are responsible for maintaining order within the Eldian internment zones such as in 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.
Brutal behavior against the Eldians by its soldiers is not discouraged, or at least is left unchecked, within the force. 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. The role and behavior of its troopers seem to make it analog to the Military Police Brigade within the Walls in Paradis.
As of Marley's decision to move against Paradis to secure its vast fossil resource, the PSA are also 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 are known to be among those chosen children. It seems the warrior recruits were subjected to pro-Marleyan indoctrination as part of their training, as Zeke exposed the identity of his parents after he was selected.
It is unclear whether or not the PSA's jurisdiction covers the whole of Marleyan society or is limited to just the ghettos. However, it does operate an oversea outpost on the coastal borderline of Paradis for the purpose of exiling undesirables into the island.
Despite its power, the PSA was 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 Krueger, 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.
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 advanced small-arm weaponry such as bolt-action rifles and revolvers.
The Marleyan security force in Krueger 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 Krueger, 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 Krueger'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 Krueger 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, Krueger 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.