The CSE citation style is a citation style created by the Council of Science Editors, a non-profit organization. They publish the CSE style guidelines in the CSE Scientific Style and Format Manual, now on the 8th edition.
There are three ways to correctly cite sources in the CSE style. They should not be mixed together (format all citations the same way).
Name-Year (N-Y): Also known as author-date, the author name and publication year are surrounded with parenthesis and placed next to the cited text as an in-text citation. The reference list at the end of the article is ordered alphabetically by the author's last name.
Citation-Name (C-N): Superscripted numbers (example: ¹) are placed next to cited text as an in-text citation. The reference list is still sorted alphabetically by the author's last name, but the corresponding in-text citation number is prepended to each reference to connect both of them together.
Citation-Sequence (C-S): Similar to Citation-Name, superscripted numbers are used next to cited text and are also prepended to the author's name in the reference list, but the reference list is sorted by the citation number in ascending order instead of the author's last name.