AP Potion 50 is an item of consumption.
This item regenerates 50 AP, it can be used when your AP isn't at his limit. If you use this potion whereas your AP is close to your limit of AP, your AP will surpass the limit restrained by your level.
It can be obtained by completing the Final Battle of each stories in Magical Girl Story Quests, Event. It can be also a reward for Login Bonus and Missions.
In the Shop, you can purchase AP Potion 50 in exchange of 
Magia Stone .
It's recommended to buy the packs containing tickets in the Magia Stone Shop, and when starting out the packs containing only potions are also worthwhile.