I think this is probably Evangeline After the Completion.
I thought he died from overwork in Korea, but when I opened my eyes, I found that I was a supporting character in a novel I wrote. Evangeline, who was executed for harassing the female lead. While running and running alone to avoid the ending of the original, he said, “I copied the author’s novel when I was creating the world. Instead, if there is anything you want, I will give it to you.” With the blessing of the damn god who invited me to this place, my beauty, abilities, wealth, and background were all ruined. Now all I have to do is wait for the happy ending. “Because she’s going to be my companion.” She tried to get along with the sculptural-looking duke’s eldest son, aka ex-boyfriend Kai Del, and said, “Evangeline will be my daughter and she’ll live with me forever.” It’s not easy because of the duke’s interference, who says she is a family treasure and wants to adopt her as her stepdaughter. No! My conclusion should be ‘I lived a long and happy life’!
An author wakes up inside the world of a novel she'd written as Evangeline, the silver-haired villainess who, as an adult, is fated to kill the blonde female lead, La Shera. At this point in the story though, they're both teenage orphans living as servants in a man's house.
They learn that one of them is to be adopted by a marquis, but it's yet to be determined which one of them it'll be. However, Evangeline knows that in the original story, she was adopted by the marquis and abused by him, and tells La Shera that they'll be miserable if they allow themselves to be adopted.
As a means of preventing either herself or La Shera from being adopted, Evangeline tells a maid who was cruel to her in the story that she can be the one who's adopted if she sings a particular song to the marquis. However, La Shera was listening to this and ends up singing the song herself, which results in her being adopted.
As La Shera is being taken away, she turns her head toward Evangeline and smirks at her. The maid then explains that La Shera had been playing Evangeline and others all along in order to receive better treatment.
While out and about in town, Evangeline meets Toas Whittaker, the ten-year-old son of a duke, and his older brother, Kydel. Evangeline is subsequently adopted by the Whittakers, which is what happened to La Shera in the original story.
There are magical elements in this story, aside from the initial transmigration. For example, both Toas and Kydel can enhance the power of their strikes with magical energy.