How can I apply Medicare part A and part B for my dependent parents
who are over 75years old, never worked in U.S. , and lowfully admitted
permanent residents since year of 2002. I have worked over 10years in
medicare-covered employment.

I am not certain of this, but I doubt that your parents are eligible
for Medicare.

Some years ago I investigated the situation regarding ways to get my
elderly father on Medicare. He had never worked, even though he was a
natural-born citizen of the United States. We were able to obtain
Medicare for him only because he had, at one time, been married for
over ten years to my mother, a person who had paid into the system. I,
too, had paid into the system; but his relationship to me, I was told,
was irrelevant.