One common scenario could be Naruto getting into dangerous battles. Kakashi might worry about Naruto's safety as Naruto is often reckless in combat. He could be constantly thinking about how to protect Naruto or train him better to avoid getting seriously injured.
One possible scenario could be Kakashi fails to train Naruto properly. Maybe he misses some crucial aspects of Naruto's development, like not focusing enough on his chakra control early on. Another could be that Kakashi fails in a mission where Naruto is involved, perhaps due to miscommunication or underestimating the enemy.
In some fanfictions, Kakashi might disguise himself as a sage from an unknown land. He would wear robes with strange symbols, have a long beard (maybe a fake one), and pretend to have great wisdom. By doing this, he can attract the attention of those who seek power or knowledge. He can then use this to his advantage, either to lead them astray if they are enemies or to guide the young ninjas of Konoha if they are friends.
In a more psychological approach, Naruto could have grown so much as a character that he no longer fears Kakashi's reputation. This new - found confidence could change the dynamics of their fight. He might be able to read Kakashi's moves better and anticipate his attacks. Combined with his own ever - improving skills, Naruto could defeat Kakashi in this state of mental superiority.
In a battle situation where they are on opposite sides, perhaps due to a misunderstanding or some kind of mind - control. Kakashi, with his superior skills, could accidentally harm Naruto while trying to subdue him. For example, if Naruto is being influenced by an enemy's genjutsu and attacks Kakashi, Kakashi might have to use a more forceful defensive move that ends up hurting Naruto.
He often keeps a close eye on Naruto. In many fanfictions, Kakashi will be secretly observing Naruto during his training or missions, just to make sure he doesn't get into too much trouble.
One interesting scenario could be Kakashi trying to teach Naruto some basic ninja skills in a fun way while babysitting. Maybe he sets up a mini - training ground in the yard and shows Naruto how to do simple jutsu. Another could be Kakashi having to deal with Naruto's over - the - top energy by telling him epic ninja stories to keep him calm and entertained.
Another situation could be that Evil Kakashi withholds important ninja knowledge or techniques from Naruto. Instead of teaching Naruto valuable skills to help him progress, he keeps them to himself, leaving Naruto at a disadvantage compared to his peers. This would be a form of abuse in the context of the ninja world where knowledge is power.
Another situation is when Kakashi is on a solo mission. He might encounter a group of powerful opponents who manage to wound him. This forces him to rely on his wits and basic ninja skills to survive while waiting for backup. It can show his resourcefulness even when injured.
Perhaps Kakashi takes Naruto to a secluded hot spring that has healing properties. He helps Naruto into the water and watches over him as the warm water soothes Naruto's injuries. Meanwhile, Kakashi shares some of his wisdom about chakra control and how it can help in the healing process. This is not only a physical care but also a mentorship moment for Naruto.
One heartwarming scenario could be Kakashi reading bedtime stories to baby Naruto. He might use different voices for each character in the story, making Naruto giggle. Another could be Kakashi teaching baby Naruto how to walk. He'd be super patient, holding Naruto's tiny hands as the baby takes his first wobbly steps. And Kakashi would definitely make sure Naruto is well - fed, cooking simple but nutritious meals for the little one.