Withholding tax applies to foreign employees living in the canton without a C settlement permit: permit B, permit L, asylum seekers allowed to work. It also applies to people living abroad who work in the canton without falling under the cross-border agreement: weekly commuters who stay in Switzerland during the week, residents of a country other than France, or cross-border workers who have not given their employer the tax residence certificate.
It ends with the C permit, or on marriage to a Swiss citizen or C permit holder: the couple then moves to ordinary taxation and files a return every year.
The deduction covers federal, cantonal and municipal tax in a single line of your payslip. Neuchâtel applies a flat cantonal rate on income, but the withholding scale remains progressive: it includes direct federal tax and an average municipal coefficient, not the one of your municipality.