Is it bad for the cat's health if I keep prodding my cat to play when she wants to rest or sleep?

Question

At times I am so deeply engaged in a play session, that even when the cat wants to stop and rest I keep prodding her for a while.

Also sometimes when I feel too bored and my cat is sleeping, I wake her up for a play. She sheepishly plays on for a minute before dozing off again.

I don't want my cat to have bad health. So am I doing it right?

EDIT:

It may be noted that cats dislike persons who are cruel to cats. In contrary me and my mother are closest ones to her.

There is no play toy. Here the mode of play is gentle wrestling. The same as between two kittens.

Here even the bed is my lap and not any sofa and couch, usually I am working and my cat is sleeping on my lap.

My cat's general routine is eating, drinking, peeing and pooping. She sleeps the rest of time.

She is not even 1% crepuscular. She is awake only when we are awake, sleeps with us under blanket in night and in deep sleep at dawn when we all sleep together.

She is always on leash. The reason being otherwise her life is in threat.

She is sometimes taken out for a walk.

Answer 1

Cats aren't toys!

They are living creatures - and like (most) living creatures they need a sufficient amount of sleep in order to maintain their health, and cats in particular sleep quite a lot (16-20 hours a day depending on their age) and are naturally awake on a different rhythm than humans are (they are crepuscular so are most alert at dawn and dusk).

About 75% of their sleeping time is quite light sleep - intended so that they can wake quickly in response to danger etc. They can wake briefly and return to such a state relatively quickly and easily, so you don't have to walk around on eggshells to avoid waking them - but prodding them awake and keeping them awake when they want to be asleep is another matter.

The behavior you describe is not only (potentially) detrimental to the cat's health it's also downright cruel. Stop it.