In a fanfiction about Kagome adopting a baby, the story might focus on how she adjusts her life. She would have to deal with the reactions of her friends, like Inuyasha who might be initially confused or even a bit jealous of the attention the baby gets. Kagome, being the kind - hearted person she is, would make sure the baby is well - cared - for, perhaps using her knowledge from her own time to provide better healthcare and education for the child.
The baby could have some special powers or a unique heritage. Kagome might discover this as she raises the child. For example, the baby could be related to an ancient and powerful demon or spirit, which could attract both good and bad attention in the feudal era.
The baby could be an orphan from a nearby village that has been attacked. Kagome stumbles upon the baby while on her travels with Inuyasha. Since she has a big heart, she can't just leave the baby there, so she takes it with her.
As Shippo grows up under Kagome's care, their relationship deepens. They go through many adventures together, facing demons and other challenges. Through these shared experiences, they build a strong bond. Shippo might start to see Kagome as a mother figure, and Kagome sees Shippo as her own family. They support each other emotionally, like when Shippo comforts Kagome after a tough battle, or Kagome encourages Shippo when he's doubting his abilities.
Another plot twist might be that Shippo's powers develop in an unexpected way. Instead of the normal growth of his fox magic, he gains the ability to time - travel. This could lead to some really exciting adventures for Kagome and Shippo as they try to figure out how to control this new power and not disrupt the timeline.
One popular fanfiction with this premise could be 'Kagome's New Discovery'. It beautifully depicts Kagome's journey after finding the baby hanyou. The story focuses on her attempts to protect the baby and find a place for it in her world.
One idea could be that the baby has a special power inherited from both of them. Since Kagome has spiritual powers and Bankotsu is a strong warrior, the baby might be able to sense evil spirits from afar and also have great physical strength. This could lead to many adventures where they have to protect the baby from those who would want to use its powers for their own gain.
One great fanfiction where Kagome finds a baby Sesshomaru could be 'Kagome's Unexpected Discovery'. In this fic, Kagome stumbles upon a baby Sesshomaru in a forest glade. The story then delves into how she decides to take care of him, despite their previous enmity. It's a heartwarming tale of an unlikely bond forming between the two.
I'm not sure of a specific titled fanfiction exactly like this, but there could be many on platforms like Archive of Our Own. You can search for tags like 'Sesshomaru', 'Baby Kagome', 'Found Family' to narrow down the results. It's likely that in such a fanfiction, there would be a lot of cultural clashes as Sesshomaru is from a very different world than Kagome, which could make for some interesting plot points.
In many of these fanfictions, Kagome is portrayed as a very protective mother. Given her kind heart and her own experiences in the dangerous world of demons, she would do anything to keep her baby safe. She might use her spiritual powers in new and creative ways to protect the child.