Well, in such a fanfiction, he might control space through his magic wand. Maybe he uses a special spell that he discovers or invents, which allows him to manipulate the fabric of space, like creating portals or warping distances.
Time control often creates mystery in the plot. In fanfiction, when a character starts to manipulate time, it might not be clear at first what the consequences will be. Other characters may notice strange things happening, like events repeating or people acting differently. This mystery can drive the story forward as everyone tries to figure out what's going on. Also, it can introduce moral dilemmas. For example, should a character use time control to save one person if it means sacrificing others in the new timeline? These types of questions add depth to the plot.
In some Harry Potter fanfictions, time - control can be used to fix past mistakes. For example, a character might go back in time to prevent the death of a loved one. It could also be used to gain an advantage in the fight against Voldemort, like getting more time to study powerful spells or gather allies.
Often, Voldemort remains the main antagonist. Even if Harry can control space and time, Voldemort's thirst for power and his army of Death Eaters are still major threats. He might try to find ways to counter Harry's new abilities or use them for his own evil purposes. For example, he could try to capture Harry and force him to use his space - time abilities to open portals to places where more dark magic items are hidden.
Maybe he accidentally finds out when he is near some magnetic objects in Hogwarts. For example, he might notice that he can make the metal keys move towards him without using magic spells he already knew. It could be during a time when he is exploring an old, forgotten part of the castle where there are a lot of metal objects and strange magnetic fields.
In some fanfictions, it could be through an accidental encounter. Maybe he was in a situation where metal objects started to react to him unexpectedly, like when he was near a bunch of keys and they suddenly started to move towards him. This made him realize that he had this strange new power.
Perhaps he has a strange dream where he's in a world made entirely of shadows and he can manipulate them freely. When he wakes up, he starts to experiment and finds out that he can actually do the same in the real world. He might start with small things like making the shadow of a quill move on his desk, and gradually discovers the full extent of his power.
Well, it might develop as a result of some new magic he encounters. There could be an ancient spell or a magical artifact that gives him the power to control sand. He then has to figure out how to use it. He may start with simple things like making sand swirl around his hand, and as he gets more used to it, he can do more complex things like creating sand barriers or even using the sand to communicate in some way.
Perhaps it's through an accidental encounter with a powerful magical plant. He tries to interact with it in a normal way but ends up influencing its growth and behavior. This unexpected event makes him aware of his unique power to control nature. For example, he might touch a withering plant and suddenly it springs back to life and starts to grow rapidly under his touch.
In certain fanfictions, Harry Potter could control animals due to his strong bond with nature. He may have an innate gift that is enhanced by his experiences at Hogwarts. His time in the Forbidden Forest, for instance, could have led to him developing this ability. He could be using his emotions and willpower to influence the animals, like projecting his thoughts of what he wants them to do in a way that they can understand, similar to how he communicates with his Patronus which has some animal - like forms.