happy new year, please is there any short cut in correcting a spelling error at a go in different html linked together, like a tab on the home page which is on all other page or it will be corrected on individual page

That depends on how you’ve got your site set up. If the content is contained within each page then you’ll need to correct it on each page. If it pulls a single resource into all pages, you only need to correct that single resource.

This is where some site creation software comes in handy. HomeSite (now obsolete) had a terrific “find and replace” option that worked across files. I’m sure other, more up-to-date programs have that option also.

Emerald Editor (what took over from Crimson Editor) has an option to do a find and replace across all open files.

A lot of the editors do have; such as Notepad++ so it shouldn’t be too hard finding a program that will do a site-wide search and replace type function.

This made me a convert to vim (tho surely other editors have the same capability):
I go to the folder with the files. Assuming everyone with the typo is an html file, I open them all:

vim -p *.html
all the files are open as tabs.

I search and replace in all tabs:
:tabdo :%s/oldword/newword/g

In other words, as others have said, get the most out of your tools by having an excellent text editor. It can do so much work for you.