Research and independent projects have become a more discussed line in international applications, and their value is frequently overstated.
What it proves
That an interest moved from words into action. The difference between saying physics interests me and chasing one question for months is visible in a file.
It also demonstrates the ability to work independently, which is exactly what a university wants.
What sets the value
What the student actually did. Standing next to a professor and cleaning and analysing a data set yourself are not the same thing, and the reader draws out that difference with questions.
The name of the institution comes second. Work done at a well known university where the student's role stayed vague reads more weakly than a project run in their own neighbourhood where the student can explain every step.
The publication question
Publishing a paper is not required and is not expected at high school level. Paid programmes promising publication warrant caution; a piece appearing somewhere unrefereed adds very little to a file.
How to find one
Starting with a teacher at school is the easiest route and the most overlooked. Writing to researchers at universities also works, though the response rate is low and many letters are needed.
An independent project counts too: finding and analysing a data set, building a device, writing software. No institution is required.
The test
Whether it can be explained. If the student can describe the project in five minutes, saying what they did and why, the project is real. If they cannot, it will not work in the file either.
The time cost
A real project takes months and shares a calendar with exam preparation. For a student whose score is below target, spending those months on the exam usually returns more.