Employer wanting me to accommodate a time zone that doesn’t exist in my state?

Hi there sorry if this is the wrong sub. My employer wants me to accommodate to the time zone change when it happens (start an hour later get off an hour later), but I am in a state that doesn’t have daylight savings – because they need the “coverage”. This makes it so I have to switch around a lot of other things, like doc appointments, etc. Is there anyway for me to get out of this? Realistically not a big deal at all, but would rather just stick to my schedule I’ve been working for the past 3 years. Thanks 🙂