Unless the content you are taking a screenshot of belongs to you, you should cite the source as usual, in order to avoid presenting someone else's ideas as your own (i.e. plagiarism). However, in APA, square brackets may be used to add clarity when a source is unusual.
So, for example, if you were citing a regular journal article it would look like:
Last, F. M. (year). Title of article: Subtitle. Journal Title, volume#(issue#), page span. doi:
If you were taking a screenshot of this journal article, I believe you would cite it the same way, except note the screenshot format following the title.
So it might look something like:
Smith, J. D. (2020). Psychology of citations: An ethnographic study [Screenshot by INSERT NAME]. Fake Journal, 3(2), 24-37. doi: 10/12345x12345
I don't think there is section in the APA 7th edition style guide that specifically mentions screenshots, so this is my best guess. It's not like taking a photograph, of which you would in most cases be the undisputed author.
TL;DR: The important thing is to clearly state when you are sharing someone else's work or ideas, so personally I would advise against citing yourself as the author of a screenshot; cite the source of the screenshot instead (e.g. webpage, movie, etc.) and merely indicate what type of source it is (i.e. a screenshot) followed the name of the person who took the screenshot in square brackets.