How does the first sentence differ from the second in the following sentences?
1) I had better zip my jacket up.
2) I better had zip my jacket up.
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The accepted form is had better do ... or 'd better do ...:
I had/I'd better zip my jacket up.
Sometimes, had is omitted:
I better zip my jacket up.
Your second sentence sounds unnatural to my ear.
Please refer to this answer on English Stackexchange.