Would you possibly tell me which one you apply?
I do not want a pen, but a bag.
I want not a pen, but a bag.
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This is going to depend on your region. Generally, in America, it would sound better (whether it is proper or not), to say "I do not want a pen, but a bag." In an older-English type area, your second example, "I want not a pen, but a bag," would probably be heard more frequently.
Both are correct, and a listener will understand your meaning when you use either, so it is up to you.
Another way to look at this is the formality of your situation. If you are in an informal context (friends, family, etc.), the first example will sound better and less "stiff." In a formal context like work, an interview, a business meeting, etc, the second example would be more acceptable.
The more you speak a language, the more you will get a feel for proper slang and usage, and it will become second nature when deciding which format to use.