As a part time employee, what are my rights?

In a nutshell, im trying to get weekends off. Reason being that I feel that since I have a disability and cannot work full time - i should not be obligated to work weekends for the rest of my working life. Im nearly 30 and have been working every saturday for the past 6 years, and im getting fed up with it. I would like to be considered "daystaff" while remaining part time and within my limited hours of availability.

All i can find online are things like accessability and benefits. nothing related to number of hours per week.... or needing to work weekends.