Studying ancient magic texts related to serpents might be a way. These texts could contain spells or incantations that can boost the power of snake summoning. Maybe there are also rituals that, when performed correctly, can expand the range of their ability, allowing them to summon snakes from greater distances. Additionally, they could learn from other magical creatures that have an affinity for snakes, like basilisks (if they can find a way to communicate safely), to gain more knowledge about snake magic.
His character might develop a more aloof side. Because he's raised by a snake, he may not be as open and friendly as in the original story. He could be more cautious and calculating in his actions.
Some characters might develop their summoning abilities through intense practice. Just like Harry practiced his Patronus charm, they could spend hours every day trying to perfect the summoning spell, gradually increasing the range and complexity of what they can summon.
There could be many interesting fanfictions involving Harry Potter and a snake. Maybe the snake is a magical creature with special powers that helps Harry in his adventures. For example, it could lead him to hidden secrets or protect him from dark wizards.
It could also be a snake from the Forbidden Forest. There are many unknown and mysterious creatures in there. A snake from that forest might be more in tune with the natural magic of Hogwarts. Harry, being the curious and kind - hearted person he is, might come across it during one of his adventures in the forest and start a friendship with it.
It could be Nagini. Even though in the original series she was more of a servant to Voldemort, in the fanfiction, she could have a different personality and form a bond with Harry.
The snake might use its ability to move stealthily. It could spy on the enemies for Harry Potter. For example, it can slither into hidden places where humans can't easily reach and gather important information.
Perhaps the snake summoner is a descendant of an ancient wizarding family with a connection to snakes. Their ability draws the attention of Voldemort, who tries to recruit them. But the summoner resists and instead uses their snakes to gather intelligence on the Death Eaters and help the Order of the Phoenix. They could send snakes into Death Eater meetings to eavesdrop and relay the information back.
Well, in certain fanfiction scenarios, the snake might have a special bond with Harry Potter. Maybe it was once saved by Harry, and now it feels a sense of loyalty towards him. The snake could then use its unique skills, such as its ability to move stealthily through the Forbidden Forest, to gather information about threats against Harry. It could then lead Harry to safety or help him plan a counter - attack against his enemies.
A snake could use its venom to attack enemies who try to harm Harry.
Well, in some fanfictions, he might find it in the Forbidden Forest during one of his adventures. Maybe it was injured and he felt a connection to it, so he decided to take it as a pet.