This page of the FF 7 Remake guide has a description of Kids on Patrol side mission, available in Chapter 8 - Budding Bodyguard.
Your job is to find five kids who went out on "patrol". You can recognize these children by large wooden swords. We have prepared maps with the locations of the children. The first kid is here.
This is the location of the second child.
Here you will find the third child.
The location of the fourth kid.
The last child is near the orphanage.
After all the children are found, you will be sent to kill Hedgehog Pie King. Head to the children's hideout and move further - you will come across Hedgehog Pie King. The enemy is assisted by other Hedgehog Pies, who love to jump up and attack you from above. Focus your attacks on one of the Hedgehog Pies and try to eliminate them as soon as possible.
After the fight, go back to the kids and you will get...
Reward: Nail Bat - a new weapon for Cloud.