How to stay productive for a wide range of time

In a title, usually the first letter of most of the words has a capital letter. However, the presentation of your title seems to work OK here!
Consider other wording, for example:
"How to stay productive over a long period of time"

I am a candidate of a significant exam this year.

I am a candidate for a significant exam this year.

The exam is approaching.

The sentence is grammatically correct. However, consider joining up your sentences to make the text flow better. For example:
"I am a candidate for a significant and important exam this year; one which is fast approaching."
OR
"I am due to sit a significant and important exam this year."

I am aware of the importance of the exam.

See above.

However, I have no motivation to endeavwork for it .¶
Also, consider joining up these last two sentences e.g:¶
"I have a strong desire to obtain a scholarship as well, but I have little motivation to work for it ."¶

Occasionally, I will be utterly productive and study for all day long.

This sentence is OK. Some people would leave out the "for" in "... study for all day long."

But this situation does not last long.

Best to avoid starting a new sentence with the joining word "but". Consider joining your sentences like this:
"Occasionally, I will be utterly productive and study for all day long, but this situation does not last long."

It perhaps maintain for 2 to 3 days, afterwards I get back to the lazy status again.

"It perhaps lasts for 2 to 3 days, then I go back to being lazy again."

My idleness has drawncauses me apprehension.

I have no idea how to get rid of it.

This sentence is OK. However, try joining up the last two sentences. For example:
"My idleness causes me apprehension, but I have no idea how to get rid of it."

I really wish I can stay productive for a wide range of time, instead for a provisional time.

Consider other possibility:
"I really wish I could stay productive for a long period of time, instead of just a short period."