Does the symbol "&" in author list mean anything? Is writing Author A &amp; Author B the same as writing Author A, Author B in the author list? 

To make it clear, this question asks about formulating the author list in the author section when publishing a paper. 

The field is computer science. Is there a way to signify that Author A is the first author?
Is writing Author A &amp; Author B the same as writing Author A, Author B in the author list? (when publishing a paper)


You don't have a choice, the journal's style guide will do it for you. In cases where there is a list and not a block (or otherwise separated), an ampersand will be used for the last author in every case I'm aware of. 



Original answer 

In citation formats I'm familiar with (e.g. APA), using a comma with only two authors is never correct. 

In other words, Author A., Author B. (2020) looks like a mistake, as if the third author (who would be separated by an &amp;) were missing.

It makes no difference with regards to who is the "first" author.