What is correct part time or part-time?

The correct form is "part-time" with a hyphen. This is used as an adjective to describe a job or position that requires fewer hours than a full-time role. For example, "She works part-time at the local café." Without the hyphen, "part time" can be used as a noun or adverbial phrase, but in the context of describing employment, "part-time" is the preferred usage.