What?

Yes!

Maybe this is before or after she has been possessed by her father?

Maybe before -- although she was possessed as a very young girl. She's killed during her possession though, so there's no after.

Not to be nitpicky, but Asenath as presented in The Thing at the Doorstep is an evil, possessed, Deep One hybrid that worships Shub. Elite monster class.

Asenath is an Ally also in Arkham Horror, so, I guess they kept the two bgs consistent