This is a tricky situation. Because of New York's convenience rule, they will contend that all of it is taxable. But that doesn't mean that it necessarily is that way. In these circumstances your income is not taxable to New York:
Your remote work for the company is not performed on behalf of the New York office. If the remote work is being performed directly for the California based company, and not their NY office, there is no convenience rule from New York. California would have to claim convenience, and they don't have that provision. You will allocate your New Hampshire working days as non-NY days, and retain documentation that shows the nature of the work was not on behalf of the New York office.
You moved to New Hampshire, qualify to file a part-year return for New Hampshire (even though they do not have a state income tax), and, after the move, did not maintain more than a de minimis physical presence working for the New York office. If after moving to New Hampshire you did not work both within and without New York, they don't have a basis in statute to claim convenience. You may follow the same technique as above to allocate New York income, and retain documentation to support your position if you need to defend it.
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