Office 2003, including Publisher, is retired and no longer available for download. If you do not have a copy on media somewhere then you won't be able to reinstall this software.
If you go searching the internet you will probably find lots of links to download Publisher 2003, including the Internet Archive. However be aware that may of these sites are actually hosting malware masquerading as legitimate software and may even actually install the actual software. But it is not recommended that you use any downloads other than from Microsoft.
Also be aware that Publisher is reaching end of life next year, Oct 2026. After that it won't be supported at all. You can read about MS's recommendations for replacements.
Alternatives are available for various price points.
- MS 365 supposedly has Publisher for some subscriptions but this is most likely for the more expensive business subscriptions. But, again, this is only until next year.
- Alternative, and possibly free, products (I've tested none of these) that can import Publisher files (depends on product and version though)
- Scribus
- LibreOffice
- Affinity Publisher