CAN MY EMPLOYER FIRE ME IF I ONLY GET PAID PER PATIENT IF I REFUSE EXTRA WORK?

I GET PAID PER PATIENT
NO PATIENT = MY TIME
DO NOT HAVE TO REPORT TO OFFICE WHEN I AM DONE FOR THE DAY JUST HAVE TO DO THE PATIENTS I HAVE SCHEUDLED FOR THAT DAY. HAVE SAME PATIENTS EVERY WEEK .
IF I HAVE 3 HOURS BETWEEN PATIENTS THEN THAT IS CONSIDERED MY TIME . NO PATIENT = NO PAY
DO I HAVE TO TAKE THE EXTRA WORK OR CAN I REFUSE AND NOT GET FIRED DUE I HAVE MEDICAL APPTS FOR MY SON IN MY OFF TIME AND HAVE TAKEN A 2ND JOB ALREADY DUE TO THEY HAVE REFUSED ME EXTRA WORK FOR OVER 8 MONTHS NOW! I HAVE ASKED FOR ANY KIND OF WORK FROM LPN WORK TO CNA. NA TO JUST HOUSECLEANING TO GET EXTRA WORK FROM THEM AND BEEN DENIED. THEY HAVE DENIED IT FOR A COUPLE OF REASONS.
1, THEY DON'T HAVE ANY BUT I HEAR OVER AND OVER THAT THEY ARE SHORT PEOPLE AND NEED HELP,
2; THEY CAN'T LET ME TAKE WORK THAT IS BELOW MY LEVEL BUT WHEN I STARTED IT WAS OK AND GAVE ME ALL KINDS OF WORK .
I WOULD LIKE TO KNOW CAN THEY FIRE ME IF I REFUSE THE WORK?