This page of our guide to Greedfall contains a detailed description of The Vices of the Mother Cardinal companion quest commissioned by Petrusa.
Where to start the quest?: Talk to the man after completing the Old Countries in the New World quest.
Travel to San Mateus. Then talk with Mother Cardinal. You'll get the opportunity to talk to her during the Trouble in Eden quest. Now go upstairs and search the women's apartments. Go down to the basement - you will need 3x Comfortable Vests, which you can buy from a nearest merchant. Equip them and then walk further down the cellars.
Search the indicated chambers and then go to the innkeeper. Now go to the prostitutes' chamber - you can bribe a guard with 50 gold pieces or use your intuition's talent. Talk to women - you can use charisma to find out more about the woman in question, but the main goal is to get information about the woman in the green coat.
The next target to be questioned is the bookmaker and then the usurer. Now you have to go to the indicated place to find Candy Cane. You have to go to the indicated place at night, so if necessary, go to the residence and let the time pass. After talking to Candy Cane, the mission will be over. You will get +3 to reputation with Petrus and 1000 XP.