Can I ask my current job to keep my information confidential with a potential employer or new employer who may call for questions?

You can ask, but that doesn't require them to do so.
Confidentiality of job information in the private sector is not specifically covered by laws (that I know of), but by each company's policy.
Because of lawsuits, however, many companies limit what they divulge to dates of employment, salary, and reason for leaving. A few even limit it to the first one only. Sometimes there are personal resentments within the company and things are said that aren't true, or are subjective, or otherwise deliberately damaging. Having a strict policy prevents that.

Your best course of action is to ask what your company's policy is, and take it from there.