This chapter of the guide to Dragon Ball Z Kakarot has a walkthrough for Master Roshi's Prized Possession side quest.
Time frame: From Attack of the Saiyans - Episode 1: A Long Overdue Reunion to Episode 1: Intergalactic Invader
Reward: 44 EXP, D Medal, Book for Grown-Ups, energetic fish, Herbs
Where to start: Master Roshi's Island, as Goku.
A very simple task. You must find Master Roshi's "book". Talk to the turtle, and he will point you to the magazines. Take them to the Master, and you will finish the task. You will also get a Soul Emblem.