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Iím just wondering if my site can get penalized if something gets syndicated to many sites even though it was published/indexed first on my site.
Duplicate content does NOT (yet) lead to a penalty, just a serious risk of the page appearing as a supplementary listing.
It's an important difference; a penalty has implications for the whole site; duplicate content removal from listing is simply subject to Google trying not to bore their searchers to death, and only involves the page at issue.
So you do need to decide if your property is worth protecting, or if you are just using it to get a link from an 'article farm'.
If the latter, do think carefully. It's usually the farm that benefits from 'syndication', rather than the author.
Often better to use quality content to build your own site, and allow people to link to it.