Another possibility is that an evil wizard from the past, who was previously defeated, gets resurrected or empowered by Harry's time - traveling interference. This wizard could then become the main antagonist, using Harry's actions to their advantage and wreaking havoc on the wizarding world.
Well, in this 'Harry Potter goes back in time' evil fanfiction, Harry might go back and change things to benefit Voldemort. Maybe he'd stop Dumbledore from finding out important information or interfere with the Order of the Phoenix's formation. He could also use time - travel to learn dark magic from the past and bring it to the present, causing destruction and fear among the wizarding community.
The main antagonist could be the Devil himself. He might see Harry as an intruder in his domain and try to keep him there forever. He could set up all kinds of traps and challenges for Harry to overcome.
It could be a dark wizard that was previously unknown. Maybe this wizard has a grudge against Harry's family for some long - forgotten reason and is using a very subtle and complex plan to harm Harry. And Fred discovers this wizard's plot when he goes back in time.
There could be a dark entity that lurks within the Durmstrang castle itself. It might have been awakened by Harry's arrival or has some connection to the school's past. This entity could manipulate students and teachers alike to create chaos and oppose Harry.
The main antagonist could be a new character, a corrupt official in the Ministry of Magic who wants to get rid of Harry because he's seen as a threat to their power. This person could manipulate the legal system to send Harry to jail.
It could be a new dark wizard who has some personal vendetta against Harry. Maybe this wizard has a grudge because Harry defeated Voldemort and he wants to prove he's more powerful, which enrages Harry and causes him to go on a rampage.
It could be a new dark wizard who has the power to manipulate minds. This wizard might target Harry specifically, driving him insane as part of a larger plan to take over the wizarding world. Since Harry is seen as a hero, if he goes insane, it would create chaos and make it easier for the antagonist to achieve his goals.
It could be Zeref. If Natsu goes back in time, Zeref might have different plans or be in a more powerful position at that time. He could be the main obstacle for Natsu to overcome, especially if Natsu is trying to change things related to the dark magic that Zeref wields.
Perhaps an ancient martial arts master who has gone astray. He might envy Kenichi's pure heart for martial arts and tries to corrupt him. This antagonist could use his deep knowledge of ancient martial arts against Kenichi, creating intense battles between them. Also, he might try to use Kenichi to gain more power in his own time period.
It could be a powerful sorcerer from the time she travels back to. This sorcerer might sense that Elena doesn't belong in that time and wants to stop her from interfering with his plans. Maybe he has some dark magic he wants to use to take over the kingdom or town she's in.