I only work 3 days a week now.. .. My Dr's office wants to hire all new staff. I have never been written up for anything, never been late, have worked for them for 3 years. My hours are going to be cut to 1 day a week. They want me to quit, instead of firing me. Do I have any recoarse?

It's up to you whether you quit or wait for them to fire you, but if you are asking if there is any action you can take to save your job, sorry but no.

if I quit for having my hours cut,, can I get unemployment?

Very unlikely. Find the new job first, THEN quit. UI benefits are meant for people who lose their job through no fault of their own or for a reason which does not disqualify them from benefits. They would not likely look kindly upon an applicant who had SOME income and chose to have NO income because they THOUGHT they were going to be discharged. Dust off the resume and start looking.

I think reducing your hours by 67% may constitute good cause to quit. The sentiment being that the employer unilaterally changed a primary condition of employement such that you could not continue to work there, hence you were forced to look for more suitable work through no fault of your own.

However, I also think your real problem is that you only work three (3) days per week, which will not be considered full-time by the Review Commission. If that is the case, then you will be disqualified on the basis of availability, ie, that you are not able, available and actively seeking full-time work.