Thanks for this essay.

Overall, it’s fine. Watch out for inappropriate word choice. Have a look at the official descriptors for IELTS Task 2 Writing (public version) here, under Lexical Resource. If it looks strange, don't use it!

Word Choice/Word Form/Usage/Tense

• Parents would like their youth to successfully pass the exam → Parents would like their children to successfully pass their exams.
• As a result, youth who find themselves in a severe competence with their counterparts… → As a result, young people who find themselves in competition with their counterparts…
• people make themselves such busy with studying  that → people make themselves so busy with studying that
• an increasing number of people get deprived from attending in colleges → an increasing number of people are deprived of the chance to attend college OR  an increasing number of people are unable to attend college /obtain a place in college
• parents should get aware of consequences → parents should be aware of the consequences
• there are many evidences → there is a lot of evidence  [evidence is non-count – just like ‘information’ or ‘research’ or ‘equipment’
• Alternatively, more investments shall be made to create more universities → Alternatively, more investments should be made to create more universities

You wrote:

• Parents should be aware of the consequences of their provocations when it comes to university participation.

‘Provocations’ is not right here/ Here’s one possible rewrite. It's got fewer nouns and it's shorter:

Parents should not push their children too hard.

However/But, Athough/But

Don’t use ‘however’ and ‘but’ and don’t use ‘although’ and ‘but in the same sentence:

However there are many evidences that suggest future success of a person is not solely dependent to university graduation, but this myth still exists among parents.

Here are some possible rewrites:

Many parents still believe that university graduation is necessary for success, despite evidence to the contrary.   OR

Despite evidence that future success is not solely dependent on a degree, many parents still cling to the myth of guaranteed jobs for graduates.  OR 

Many parents believe that a university education is a must for success. However, many…

Punctuation

Remove the unnecessary comma. Don’t separate the subject (‘young people’) from its verb ('try'):

Young people who find themselves in competition with their counterparts, try to increase their chance by over-studying.

Here’s one possible rewrite:

Young people who find themselves in competition with their counterparts try to increase their chance by over-studying.

Conclusion

You only have one sentence in your conclusion. This means it has to do too much work. A conclusion should summarize both sides, give your opinion and perhaps look to the future (advice or suggestion or recommendation or prediction.) You can read more about conclusions here. I recommend at least two sentences.

There is a problem with the comma after ‘situation.’  Summarize your suggestions

To sum up, I believe many young people according to their situation, lessen their leisure time to study more which is abnormal and should be corrected.

Here’s one possible rewrite. Break up the sentence, summarize your ideas and look to the future:

To sum up, I believe many young people are under too much pressure from their parents and from inadequate education systems.  More investment and more realistic expectations from parents would mean a more enjoyable educational experience for young people.

Give reasons for your answer and include any relevant examples from your own knowledge or experience.

Some young people make themselves such busy with studying that they cannot find an hour as a leisure. In this essay I will discuss some sample reasons which might result in this behavior and suggest some solutions to reduce this imbalance.

Parental pressure is one the most obvious reason which oblige children to add more time to their studies. Parents would like their youth to successfully pass the exams and eventually attend in higher educations. As a result, youth who find themselves in a severe competence with their counterparts, try to increase their chance by over-studying.

Another reason is the fact that the number of people who are accepted for higher educations is limited. Financial restrictions don’t permit public or private universities to expand students seats regularly. Therefore it is normal that an increasing number of people get deprived from attending in colleges each year.

To solve this problem, parents should get aware of consequences of their provocations when it comes to university participation. However there are many evidences that suggest future success of a person is not solely dependent to university graduation, but this myth still exists among parents. I think a country’s educational system can deliver crucial information to parents in this case. Alternatively, more investments shall be made to create more universities so that the unhealthy competence between people on university entrance gets eliminated.

To sum up, I believe many young people according to their situation, lessen their leisure time to study more which is abnormal and should be corrected.