Is it good for SEO to add same word in indifferent case to match all possible search key word. Like
<meta name="keywords" content="shoe, Shoe, SHOE ">
Is it considered good or duplicate?
Ditch the meta-keyword tag, or at the very least, ditch the same repeating words regardless of whether the letters are upper or lower case. Google doesn't pay much attention to meta-keywords and I believe Bing will use them against you if they are used the way you do. You're trying to rank for a keyword in an artificial way.
The only meta tag you should use to add the relevant keyword only once to is the meta description tag. For example:
<meta name="description" content="Find out how large black shoes are made">
And if you really need to rank for shoes, maybe find another word close enough to it you can use in your description. For example:
<meta name="description" content="We sell shoes, and other footwear in our large online store">