There is a difference in meaning between the two. '' I should still be here by Thursday"' = let's that you are leaving town, but not before Thursday. ''I should still be here on Thursday"= Let's say that you are leaving town, but definitely not on Thursday, may be Friday or so.
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PreciousJones I should still be here by Thursday. OrI should still be here on Thursday.Are both useable?Thanks!"By" is just barely conceivable, but you normally see that the other way around: I should have left by Saturday, but I should still be here on Thursday. "By" would be more for an occurrence, and your simply not leaving is not an occurrence.