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If you mean a script running on the result page, depends exactly what you want to do but you can inject scripts in a formula result column.

<@U29QCJQF3> thanks.
yes, I mean script running on the result page.

I want to add a field and button to that page and attach a function to that button.

You could add a button to every result line by putting it in a formula

To get just a single button at the top is probably technically possible with DOM manipulation but I wouldn't recommend

The supported way to do this type of customisation is create a suitelet to display your search results