This chapter of the guide to Dragon Ball Z: Kakarot has a walkthrough for A Father's Dignity side quest.
Time frame: From Majin Buu Reborn - Episode 8: Finale to No time limit
Reward: 249,984 EXP, D Medal, Super Awesome Book for Grown-Ups, Fancy Urn
Where to start: Southeast Mountains Area, as Gohan.
Talk to Mr. Satan and then go to the edge of the city. Your goal is to kill one of the dinosaurs. If you have a team with you, they will help you in the hunt.
Collect the items and go back to the quest giver. This will complete the quest.