Is there a time travel story with this plot?

Last night I had trouble sleeping, and started thinking about the lengths people go to in order to look and feel younger. Somehow my thoughts meandered along a path until I arrived at time travel.

What if the best way to look and feel younger is to be younger?

The way you’d do this, of course, would be to have someone go back in time to the day you were born, and kidnap your mother while she was in labor. Then, you’d obviously need to have her brought forward a few years in time, how ever much younger you wanted to be, and keep her there until you were born. It got fuzzy after that; I couldn’t decide if your mom would need to stay in the to-her future with you (maybe the whole family would be time-napped) or if baby you’d be given to the to the then-present her (who would likely be bewildered that the then-present you had disappeared in place of your baby self) before returning to her original timeline.

Or, maybe your mom doesn’t need to be in labor and you could just be kidnapped as an infant and traveled forward in time all by yourself. Like I said, it got fuzzy.

Can you think of any stories - from any sort of media - that are close to this? Keep in mind the whole point of the time travel is to change a character’s age.

The only thing I can think of even remotely like this is All You Zombies, because it involves time travel and babies, but not really close at all given the plot not having anything to do with trying to be younger and all to do with being your own mom and dad.

How could the “you” being born a few years later be the same “you” that traveled back in time, conceived in other circumstances, maybe by a different father, but definitely by a different sperm and egg?

There is. It was published in June 2038. The odd thing is, there were several writers credited with being the author at different times.

You’d of been conceived in the same circumstances. The time travel is to when your mother was already pregnant or you’d already been born, not before then.

Ok, nevermind, I hadn’t read your OP carefully enough.

Todd Thromberry?

I wrote this story in the 50s, and sold it to Thrilling Wonder Stories. After it was optioned by Spielberg, I went on a whirlwind book-signing tour, oblivious to the fact that George had cast an unknown carpenter named Ford to play my character in a three-film arc (I said “No Way” to any prequels).

But you might not know any of this. See, this was the other me, in that other timeline…

Vaguely similar: a YA series “The Missing”, by Margaret Peterson Haddix. I believe there were 8 books in the series, and read them many years ago.
Not to spoil the plot, but it involves famous children and babies who are in grave danger, brought to the future in order to save their lives. The children have no recollection of their previous time line.

From Wikipedia: The Missing is a series of fictional young-adult novels written by Margaret Peterson Haddix. It tells the story of famous children from history stolen by futuristic time travelers from their place in time and accidentally sent to the 21st century as babies. They are then adopted by families in the 21st century.

Even the best time travel stories tend to contain paradoxes that break down under scrutiny (see: Back To The Future), but if they’re entertaining and well-written enough, you don’t think about it until later, and/or you don’t mind hand-waving it away.

I think a story about moving a baby (or fetus) forward in time so that the adult version would become younger would create so many logical hurdles that it would take some serious writing chops to pull off at all coherently.

I’m not saying it couldn’t be done, but there’s probably a good reason you haven’t seen such a plot before.