Then I'd look into a custom written script. A possible problem is that it would need to know where each chapter starts!
Here is the easiest use case: manually select each chapter's text one at a time, run script. The script subtracts the correct amount -- found through the first superscripted number in that selection -- from all the superscripts in that selection.
That'd be fairly straightforward to write as well as rather safe to run (I'd try to make it reject numbers out of range), but it hinges on this: (1) Can you select the consecutive text for each chapter? Or -- a worse case -- does the text live in non-contiguous, non-threaded text frames? (2) Do you have not too many chapters? I imagine it would be no bother for up to 10 selections, and more manual work for 10 to 20 chapter, and a real bore for yet more than that. On the plus side, you'd only have to do this once per book, and the script itself ought to be very fast on each selection.
Hold the press, I have a better idea!
All that it requires is a list of the first superscript number per chapter. Then, this (as yet) hypothetical script can simply go over each styled number and find out the correct value by looking it up in that list. ("Hypothetical", only at the moment. I need to stuff a bit o'food in my gullet but will give it a go somewhere tonight.)
(Oof ... just one night later and this is on the 3rd page of questions. Perhaps it's easier to post a question here than to find something in the Online Help?)
Adjust the top two variables in the following script to your document's needs: fill in the exact name of your "Note" character style, and the current number of the first note for each chapter. Then run the script.
Best is to first test it on a copy! If something goes wrong, there may be no way to restore the original text. Even if you think "ah then I'll just Undo this", you may find that there are too many changes – it's rare but I have hit the Undo Stack limit in the past –, or InDesign crashes, saving the 'current' state in the mean time, and when reopening you'll find the changes are committed and no longer can be un-done.
With the above firm in mind, here is the script. I didn't have any suitable sample with the same characteristics so I had to construct an artificial test case, but it worked correctly on that.
// ------ adjust these for your document
var firstPerChapterList = [ 1, 4, 7, 11 ];
var characterStyleName = "note";
// ------ then run the following code
app.findGrepPreferences = null;
app.findGrepPreferences.appliedCharacterStyle = app.activeDocument.characterStyles.item(characterStyleName);
app.findGrepPreferences.findWhat = "\\d+";
list = app.activeDocument.findGrep();
firstPerChapterList.sort(function(a,b){ return b - a; });
while (list.length)
{
item = list.pop();
value = Number(item.contents);
for (i=0; i<firstPerChapterList.length; i++)
{
if (value >= firstPerChapterList)
{
item.contents = String(value - firstPerChapterList + 1);
break;
}
}
}