I thought the name of the story was Blood Born but I can't find it so I think I was wrong.
All I can remember is Sesshomaru has a son born through his blood & power. He chose Kagome to raise him. Kagome named the pup & the name was very similar to Sesshomaru's name. I think at one point in the story Koga shows up and the pup bites him. I would really like to read it again. Oh & I'm pretty sure it was rated either M or MA.

Sounds kind of like "Bound to Love By Blood"?

www.fanfiction.net/s/5097375/1/Bound-To-Love-By-Blood
Sesshomaru has a son, of pure blood. No mother. When the demon who is supposed to nurse his pup dies he goes looking for the miko! Everyone is shock, what is Kagome to do with a baby. Why is Sessshoamru watching her, will his pup bring them 2g?

Would be rated MA here (I think), so no YIM.

Hola!

Tal vez el fic que estés buscando sea este:

Bound To Love By Blood » by brandypandyxxx
Sesshomaru has a son, of pure blood. No mother. When the demon who is supposed to nurse his pup dies he goes looking for the miko! Everyone is shock, what is Kagome to do with a baby. Why is Sessshoamru watching her, will his pup bring them 2g? REWRITING! NOW!
Supongo que aquí en el site el rating sería MA.

www.fanfiction.net/s/5097375/1/Bound-To-Love-By-Blood

Yes that's it thank you both so much!