The phrase "change my fate" is correct and usable in written English.
You could use it to express the idea of wanting to alter a situation or the outcome of events that are yet to be determined. For example: "My luck has been pretty bad lately, so I'm desperately hoping I can change my fate."
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"I would hope that the result would not change my fate.
– Jay Asher, Thirteen Reasons Why Perhaps I could change my fate, but in the end, I realized, my destiny may have already been written.
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And he made me change my perspective on fate: if you win, you deserve to win.
[Update: "Community" has been renewed, but that doesn't really change my thoughts on the fate of cult shows, which I discuss below.].
However, fate decided to change my plans again, as happened in 2006 with the unexpectedly early inclusion of The Journal of Headache and Pain (JHP) in PubMed/Medline.
"The US election results can potentially change the fate of my country," said an Iranian journalist based in Tehran.
I didn't know if it was meeting someone who had the power to change the fate of my life -- he didn't know how drastically -- or the expired tags on my '91 Accord and the fear that I would be stopped, car would be towed and I would miss the meeting since I didn't even have enough money to take a cab.
"My anxiety will not change the fate of this fish".
"Thanks to the Sara Club, I am able to share my story with many who are suffering and do not know how to change their fate," she said with a beaming smile.
The trip didn't change his fate.
But for all that they couldn't change their fate.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com