Schools in New York City and the Long Island suburbs will receive hundreds of millions of dollars in new state school aid this fiscal year as part of a deal between Gov. David A. Paterson and state lawmakers that increased total school aid by a record $1.75 billion. The deal kept intact the school financing formula created last year by Gov. Eliot Spitzer and the Legislature in response to a long-running lawsuit over disparities in education spending in poorer districts. Most of the new spending will be subject to a state formula that emphasizes goals like teacher education and reducing class size.