Well, Harry might use his magic to make the baby laugh. For example, he could turn the baby's rattle into a little magical creature that dances around. He'd probably also be very protective, like how he was with his friends at Hogwarts.
Well, Naruto might be really confused at first. He's from a world of ninjas and suddenly has to take care of a baby wizard. He'd probably use his ninja skills to protect Harry. For example, he could set up traps around the house to keep bad guys away. And he'd surely try to feed Harry some ramen, which might be a bit strange for a baby used to wizard food.
He becomes more nurturing. Taking care of a baby forces him to be gentle and patient, which are new traits for him. He might also become more responsible as he has a new life to look after.
Maybe it's the child of one of his friends or allies. For example, it could be the baby of Ron and Hermione. Harry would then be taking care of the baby out of loyalty and friendship.
Naruto would use his Sharingan - like observational skills. He's used to being aware of his surroundings in the ninja world. So he'd be on high alert for any danger. If any dark wizards came after Harry, Naruto could use his speed to get Harry out of harm's way quickly.
Harry might first try to figure out what's wrong. If the baby is hungry, he'll quickly get a bottle. If it's a wet diaper, he'll change it. Sometimes, he just holds the baby close and rocks it gently, humming a little tune. He doesn't get frustrated easily because he really cares about the baby.
One possible plot could be that Harry discovers a time - traveling accident has brought baby Snape to his present. Harry, being the kind - hearted person he is, takes it upon himself to care for the baby. He has to figure out how to feed the baby, keep him clean and comfortable. Maybe he also has to protect baby Snape from any threats in the wizarding world that might target Snape even as a baby.
A heartwarming moment could be when Harry takes the baby out for a walk. He pushes the stroller carefully, talking to the baby about all the things they see around them, like the colorful flowers and the friendly squirrels. And at night, when the baby has a nightmare and Harry stays up all night comforting it. He rocks the baby gently and whispers soothing words until the baby calms down and falls back asleep.
In this fanfiction, perhaps Harry could struggle at first with the basic tasks like feeding and changing the baby. He might make mistakes but learn quickly.
One possibility could be that Draco is forced into taking care of Harry due to some magical circumstances. Maybe there's a spell gone wrong that makes it his responsibility. He initially resents it but as he spends time with baby Harry, he starts to see the innocence in him and develops a soft spot.