Does my business has nexus to California that I need to file…

You will have sales tax filing requirement in California , but not income tax . Amazon is also a marketplace facilitator and will be collecting the sales tax on your behalf

while should I file income tax to Delaware?

According to Delaware , the mere fact that you have a company registered there does not mean you have income tax nexus , therefore Delaware exempt most companies registered in that state from filing a state tax return.

Are you using an LLC ?

If you answer Yes or True to all of the questions below , then you do not have to pay taxes to the US .

1. You do not have any physical presence in the US - bank account and just forming LLC do not count as physical presence

2. You do not have any employees or sales agents in the US

3. You do not have warehouses or offices on the US - Amazon warehouse do not count as an office

4. You did not receive a 1099-K or any tax form from payment processor or e-commerce marketplace

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However, you are required to file information form 1120 and 5472. See article below

https://oandgaccounting.com/foreign-owned-us-llc/7-common-questions-about-foreign-owned-u-s-llcs-answered-by-a-cpa/

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However , SALES TAX may apply to your case. See below

If you are shipping to a buyer to a specific state in the US, then you will ONLY be required to register in those specific states once your sales reaches a threshold in a specific state.

For example, most states required that sales threshold of 200 separates sales or $100k threshold (whichever comes first) be met before registering for sales tax permit in those states

Review the link below for all the Sales Tax Nexus States and Threshold

https://www.salestaxinstitute.com/resources/economic-nexus-state-guide

which country are you from ?

which state are you located in?

So you will pay state income taxes to NC

The initial question is answered , you may need to accept this answer and post this question on a separate thread