If that $1 of interest income was earned from a US source or a foreign source, then you would not deduct it from your Federal tax return. Your Federal return taxes all of your worldwide income regardless of where you lived at the time it was earned.
You could change your part-year state tax return by either adjusting the number where you can allocate income that pertains to your part-year state, or by making an entry in the 'subtractions from income' category that you may find as part of your state tax return.
If you share the state you are filing someone may be able to give you more specific guidance about how to make the adjustment for your state return.
@Fou65000
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