What are the correct abbreviation of words "section" and "sections" in a scientific writing?
Sec. and Secs.
Sect. and Sects.
In my experience you should avoid abbreviating it (in papers, textbooks and theses). Some style guides avoid abbreviating "figure", "equation" etc. even though those are much more common. On the rare occasions an abbreviation is used, it's never "sect." but "sec." (and in a few old texts, just "s."). "Sec" is an (incorrect) abbreviation for second, and "sect" is another word; neither is likely to lead to actual misunderstandings but can mean a sentence is unintuitive at first glance.