Colour fringes on black type: what overprint preview can show
How can you distinguish between plate misregistration, four-color black, and overprint settings in small text?

If you see a blue or red shadow along the edge of fine black text, first check the color separations. For small text composed of four colors, each printing plate must align perfectly at the same point. When the plates shift slightly, these colors become visible along the edges. Sharpening the image will not address the root cause of the issue.
View the black plate in isolation.
For small text, verify the single-channel black value recommended by the printer. In the Separations panel, toggle the channels other than black one by one to see which plates contain the text. Then, enable the overprint preview to examine how the text interacts with the background beneath it. The ink composition for large black areas is a separate consideration.
If overprinting is accidentally left enabled—especially for white text or logos—the final output may differ from what was intended. Perform the same separation check on the PDF intended for the printer, and report any suspicious areas by specifying the page number. This allows the printer to know exactly which text and background combinations to verify.