Exam boards and recruitment portals usually ask for two files with different rules: a photograph in one size band and a signature in a much smaller one. Missing either means the application is refused at the last step.
A signature is a small amount of dark ink on a large pale background, which ought to compress beautifully. It usually does not, because people photograph it in poor light and the background arrives as a field of faint grey speckle. Compression has to store all that noise, so the file stays stubbornly large and looks worse the harder you squeeze it.
The fix is at the photography stage, not the compression stage. Even light with no shadow across the paper, the camera square on rather than at an angle, and a tight crop that excludes the desk. A clean white background compresses to almost nothing and leaves the ink sharp.
If you would rather not photograph paper at all, you can draw the signature directly and get a clean file with no background to compress in the first place.
Do the photo with Passport photo to get the right pixel size, then compress it to the limit. For the signature, sign on plain white paper with a dark pen, photograph it in even light, crop it tight with Crop & rotate, and then compress it to the stated size.
Most forms give a small limit for the signature, often 20 to 50 KB. Type the exact limit in kilobytes, choose JPG, and check that the result is still readable before you upload it.
Usually shadow across the paper. Photograph it under even light, or hold the camera square on rather than leaning over it.
Yes, and a scan is usually cleaner than a photograph. Crop tightly afterwards either way.
Crop tighter. Most of the file is background, so removing the empty paper does more than any quality setting.
Yes. Save the PNG, then run it through Compress to a size and choose JPG. The transparent background turns white, which is what most forms expect.