The Public Security Authorities was responsible for maintaining order within the Eldian internment zones such as Liberio on the continental mainland. It included restricting movement in and out of the ghettos, countering Eldian dissident movements, and sending undesirable Eldians to Paradis Island where they were turned into Pure Titans. During emergencies, it was also responsible for evacuating casualties and restricting access to combat areas. Its soldiers were armed so they could assist in fighting within the internment zones.
In the year 830, due to Marley's decision to move against Paradis Island 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.
At some point, the PSA had been infiltrated by Eren Kruger who was an Eldian spy known as "the Owl". During his time within the organization, Kruger was able to steal historical Eldian documents and supply the Eldian Restorationists with funds and weapons.
PSA personnel were only seen in and around the internment zone, suggesting that it was their sole area of jurisdiction. However, it does share the use of a wharf located in the coast of Paradis Island with the military, with the PSA using it for the purpose of exiling undesirable Eldian prisoners into Paradis Island and the military uses it to dock heavy transport ships.
The PSA turned 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 death did not seem to hurt his career, as by the time of Grisha Yeager's exile to Paradis Island he had attained, or still kept, the rank of Sergeant Major. To crush the Eldian Restoration Movement, the PSA also did not shy from using torture methods to obtain confessions from captured dissenters. When he was being interrogated, Grisha had all his fingers cut off by the PSA.
Others, however, show more decent attitudes, or even genuine care, for the people under their watch, with whom they became familiar with due to the day-to-day interactions. For example, in the year 854, there were a pair of gate guards who were close enough with the Warrior candidates that they often made small talks during the latter's daily passages from the gate. They were even aware of Falco Grice's affection toward Gabi Braun, and that Falco routinely visited the hospital. During the attack on Liberio, the duo tried to stop Gabi from running into the fighting at a street checkpoint, urged her to go home for safety instead. When they suddenly came under attack by Survey Corps infiltrators, one of the guards pushed her away from incoming fires before both men were shot dead by Sasha Blouse.
The PSA uniform consisted of a soft edge peaked cap with a leather visor, a trench coat, a "Sam Browne" style leather belt, a shirt which was worn with a black tie, and a pair of leather jackboots. Its troopers were 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.
The PSA operated at least one steamboat for transportation to the coast of Paradis Island where an outpost was located, though the boat was later destroyed by Kruger. The outpost itself was built with a pier by the foot of a 30-meter wall surrounding a small segment of the coastline.
Although it was unclear when the Public Security Authorities was founded, Marleyan persecution of Eldians 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 vow 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 Island where they were converted into Titans.
In 817, PSA Sergeant Major Gross murdered Faye Yeager, Grisha's sister, feeding her to his sons' dogs. 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 Island 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 officers shipped the prisoners to a borderline outpost in Paradis Island 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.
The PSA assists the Marleyan military both in evacuating casualties and preventing civilian access into combat zones during the Raid on Liberio. The lightly-armed soldiers fare poorly against the Survey Corps attackers. At least two troopers were killed in an ambush.
After Eren Yeager reveals his intentions to destroy all life beyond Paradis Island with the Colossus Titans, the Eldians inside Liberio's internment zone amass around the gate to warn the PSA about the threat. The PSA soldiers were unconvinced and start to round up the Eldians for conspiring to escape but one of them begins to retaliate. The PSA soldiers guarding the Liberio Internment Zone were unable to contain the Eldians within, with many escaping by railway and spreading the panic to Marleyan citizens.
Seeing as the Rumbling wiped out the entirety of the world's military (which was assembled to destroy the Rumbling), it can be assumed that the PSA were also killed by Eren and the Colossal.