Read the story in grade school, possibly in a children’s magazine (1980-1992). All I remember is scientist invented a way to jump into your future self and sent someone ahead then brought them back. Problem was the traveller died before the time he jumped to. Story ended with the traveller explaining that to the scientist but is shrouded by smoke. Smoke clears and the scientist screams.

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I think this is The Last Paradox by Edward D. Hoch published in 1958. I read it in 100 Great Science Fiction Short Short Stories which was first published in 1978.

In this story, a scientist has a machine that sends a time traveller into their own future.

This is a very short story, so I'm going to edit the quotes heavily or I'll be quoting most of it.

There's a setup where the professor explains to the traveller how the machine works. This matches your description: the time traveller changes their age, rather than being transported to a different year.

We now know that in this machine, we can now increase or decrease the age of an animal, in much the same way as the age of a traveller through space would change as he approached the speed of light. … You're 28 years old now and in a moment you'll be 35 years older, you'll be 63.

It goes wrong in the way you describe, complete with smoke to conceal the reveal:

"Professor, I died at the age of 60, and there's one place from which even your machine couldn't return me. One place where there is no time."

And then smoke cleared a bit and Professor Fordley looked into his face, and screamed.

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