These are called ‘Specials’ and you can see more and read about them (including how to interpret the inscriptions) on the Sydney Living Museums webpage. Here is an excerpt:
Around the world, police forces followed established conventions when taking mugshots. But Sydney police in the 1920s did things differently. Suspects hold handbags, papers, cigarettes and conversations. This deviation from protocol creates images suffused with the suspect’s personality, not unlike a commissioned studio portrait – if you ignore the backdrop of cell doors.
The people in the Specials photographs were yet to have their day in court, and some were never found guilty. Most of the Specials were taken outside the holding cells at Sydney’s Central Police Station. The police photographer positioned his camera to make the best use of available light and placed a bentwood chair in the frame to give an idea of the suspect’s height. The lack of signs that the person was in custody, such as handcuffs, meant the images could be shown to a witness during a criminal investigation without prejudicing the person against the suspect. Information, including the date, the suspect’s name (occasionally misspelt) and references to previous convictions, was sometimes inscribed onto the negative.
For further reading this blogpost also does a good job at explaining the exhibition