This is not something that can directly be set in Illustrator.
Depending on your specific needs, you may use SVG files which should be recognised by all common web browsers nowadays.
If you instead are dealing with raster graphics, you'd have to create different versions of your banner and make sure to display the appropriate ones depending on the specific devices and their screen resolutions. Or you may rely on proper scaling capabilities of modern web browsers. Anyway, this is a matter of coding, not something you can set in Illustrator.
In any case, this is still a demanding task, given the fact that there are so many different devices in use. Even the most professionally created (so-called responsive) websites do sometimes look weird on some devices due to unexpected or overlooked conditions.
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