To restrict the resulting image to a maximum file size, you can use the commandline parameter -define jpeg:extent=max_value
, like this:
convert original.jpeg -define jpeg:extent=300kb output.jpg
convert original.jpeg -define jpeg:extent=300kb -scale 50% output.jpg
convert original.jpeg -define jpeg:extent=300kb [...other options...] output.jpg
Note, this will not always work to match the exact size you wanted. You may have asked for 40kb output size, where input is 300kb, and get a result of 48kb.
(Update/Clarification: Output file size may be a bit lower or higher than your file requested size.)