How does one proceed when publishing a research paper to refute the conclusions of another (someone else's) research paper?
Showing that something in the literature is shaky or incomplete or mistaken is part of how science advances.
If you can replace a published claim with something better rather than just showing that it's wrong, all the better.
When you find an instance of that you write it up carefully, professionally and kindly and submit it to an appropriate journal - perhaps the one that published the original work.