Do I need to add jQuery in the index.html such as the following?

no, you import jQuery as a module and that's it, no global pollution needed

If I put jQuery functions in a separate javascript file, do I need to write this ?

from Python you import jQuery as module as shown in my example

Most people use jQuery to simplify the coding in JavaScript or even TypeScript. So I wonder if it is possible to mix jQuery with PyScript to simplify the coding process.

I might not understand your question then ... do you need jQuery in Python or you just want to add jQuery with JavaScript?

In both cases using a module is more 2024 and less 2000 but if you have other JS scripts that relies on the fact a global $ reference exists, then your script with integrity on the page would be the old way to go.

I just found out PyQuery for Python so it looks like I don't need to directly embed jQuery javascript into the HTML documents.

PyQuery

my first example literally gives you jQuery as it is in Python ... you never need to directly embed jQuery into the HTML document, my example shows that via a config.toml, no jQuery on the page, not on the HTML, not on the dom, nowhere ... it's a JS module imported into Python. I think I've done a very bad job at explaining what is that example, it's 100% jQuery on Python, no indirection whatsoever.

I followed your example but did it in VS Code in my local environment. I got warning in the main.py which cannot resolve the "pyscript.js_modules.JQuery" even though I setup the pyscript.toml exactly like yours.

I have already included the stylesheet and module under and also included following statement in the index.html

what you see on PyScript .com is the current PyScript version importing jQuery and there's nothing special in there. If you can't import from pyscript.js_modules it's very likely you are using a very outdated version of pyscript.

The live example that works in PyScript .com has an index.html file that shows you how to use latest PyScript in your project too.

There is no "work on my machine" here because we have tons of tests around modules and we use modules ourselves so I'd be very surprised to learn you doing exactly the same would not work in there ... unless you are running code in a worker and you forgot to enable special headers to do so, all explained in our documentation though.

Can you please show me your HTML page or how are you bootstrapping PyScript in general?