Should there be a space between a time and a.m. and p.m. in both prose and works-cited-list entries?
Yes. In MLA style, there should always be a space between the time and a.m. and p.m.:
Responding to the MLA Style Center post “Apostrophes,” Doug asked, on 30 March 2018, at 1:16 p.m., whether one should write “Albert Camus’ novel or Albert Camus’s novel.”
Doug. Comment on “Apostrophes: One Mark, Three Ways.” The MLA Style Center, 30 Mar. 2018, 1:16 p.m., style.mla.org/apostrophes-three-ways/.