I think that everyone associates it with Dostoevsky's book, but I haven't read it yet, so couldn't say a word about it.

The thing that I wanted to write about is just a lbittle of a story about a man who was in a shortage inof money.

He was badly depressed about poverty and thought that the only chance to goet out from this situation is to rob a bank.

(regarding the half of the sentence I critiqued "and thought that the only chance to get out of this situation is to rob a bank." You can also say this.

After he deciced that he had to prepare for it, and after he gathered himself mentally, he went into a bank with a pistol...

After 20 minutes, he was caught by the policemen, and the case camewent to court where he was tried.

At the trial he pleaded not guilty, but the prosecuting lawyer produced a very strong case against him and the jury passed the verdict of guilty on the accused.

While the judge was thinking about the sentence, the robber was totally frightened, b. But, after a brief deliberation, the judge, and the first man of the court started to speak and the robber was convicted of the felony.

The judge sentenced him to 10 years in prison, a. Although, the guilty man was hoping to be acquintted of the punishment.

After he went to jail, he was released, h. He served only 5 years, because he ended up getting time off for good behaviour.

I think that everyone associates the title with Dostoevsky's book, but I haven't read it yet, so couldn't say a word about it.

I agree with the other person who has offered corrections that "everyone is familiar with" is the most natural way to convey this idea, but I've offered here an alternative that sticks closer to what you actually wrote, which would also be perfectly natural, albeit slightly more formal in register.

The thing that I wanted to write about is just a little of story about a man who was in shortage i on money.

He was badly depressed about his poverty and thought that the only chance to goet out from this situation iwas to rob a bank.

I added "his poverty" because, without "his" it sounds like he was depressed about poverty as a general problem in the world. It would be understood in context of course, but I think "his" adds useful clarity.

After he deciced thatmade his decision, he had to get prepare for it and after hd. He gathered himself mentally heand went into a bank with a pistol...

"Decide" and "prepare" on their own are not incorrect, but "make a decision" and "get prepared" sound more natural. I deleted "after" to make it less repetitive.

After 20 minutes later, he was caught by the policemen, and the case came to court where he was tried.

Again, deleted "after" to reduce repetition. Just a question of style.
It is more common to just say "the police" both to refer to the abstract category as well as to groups of specific police officers. In addition to being more common, it has the benefit of being gender neutral, since there are many female police officers.

At the trial he pleaded not guilty, but the prosecuting lawyer producedor presented a very strong case against him and the jury passed the verdict of guilty on the accused.declared him guilty.

The judge sentenced him to 10 years in prison, aAlthough the guilty man was hoping to be acquintted of, the punishmentjudge sentenced him to 10 years in prison.

It sounds more natural to me to just say "acquitted," though if you want to say what he would be acquitted of, he would be acquitted of the crime, not the punishment. In which case you would write, "he was hoping to be acquitted of robbery."
I switched the two clauses. I think putting the "although" part first puts the emphasis in the right place and flows more logically. I find it difficult to explain why exactly.

He had no accomplice.

This is not incorrect, but "He didn't have an accomplice" would be more natural.

After he went to jail, he was released, he after serveding only 5 years, because he ended up getting time off for good behaviour.

I am not for or against long prison sentences, because I do not have information about the topic and I have never learnstudied law.

I think that everyone hassociate heard of Dostoevsky's book, but I haven't read it yet, so I couldn't say a word about it.

The thing that I wanted to write about is just a little of story a man who was in shortage i on money.

"short on money" is a very common phrase but not for formal writing

He was badlvery depressed about poverty and thought that the only chance to goet out from this situation isof his poverty would be to rob a bank.

AfterOnce he decicded thatis, he had to prepare for it and after he. Then he mentally gathered himself mentally heand went into a bank with a pistol...

I broke it into two sentences to make it easier to read.

At the trial he pleaded not guilty, but the prosecuting lawyer produced a very strong case against him and the jury passed the verdict of guilty on the accusedconvicted him.

"pleaded" may also be correct...

While the judge was thinking aboutconsidering the sentence, the robber was totally frightened, but ascared. After a brief deliberation the judge, and the first man of the court started to speak and t. The robber was convicted of the felony.

I'm not sure what "the first man of the court" means. If it's the same as the judge, just leave the whole phrase out.

The judge sentenced him to 10 years in prison, aAlthough the guilty man washad been hoping be acquintted of, the punishmentjudge sentenced him to 10 years in prison.

There are many ways this sentence could be arranged.

After he went to jail, he was released, he served only 5 years, because he end up getting time offHe served only 5 years of his sentence, because he was released early for good behaviour.

I think that everyone associateis familiar with Dostoevsky's book, but I haven't read it yet, so I couldn't say a wordnything about it.

"associate" doesn't make much sense here. I think what you're trying to say is that people are familiar with Dostoevsky's book as in they know it well.

Instead of saying "I couldn't say a word about it," it would sound more natural to say "I couldn't say anything about it."

The thing that I wanted to write about is just a little of story about man who was in shortage in of money/ didn't have much money.

He was badly depressed about being in poverty and thought that thehis only chance to goet out from tof his situation iwas to rob a bank.

Be careful about changing tense mid sentence. I changed your sentence to past tense to keep it consistent. I also used 'his' because it feels more natural in this situation.

After he decicded to do that, he had to prepare for it and after he gatheredhimself and, collecting himself mentally, he went into a bank with a pistol...

Using after twice here is quite clunky, I added a gerund to clean it up a bit.

After 20 minutes he was caught by the policemen, and the case came tobefore the court where he was tried.

At the trial he pleaded not guilty, but the prosecuting lawyer producedor made a very stong case against him and the jury passed the verdict of guilty on found him/the accused guilty.

"Passed the verdict of guilty on the accused" is extremely formal and doesn't fit. If you want to preserve its formality you could say "found the accused guilty" but the regular way to say it, even in literary works would be "the jury found him guilty."

While the judge was thinking about the sentence, the robber was totalextremely frightened, but after a brief deliberation, the judge, the first man of the court, started to speak and the robber was convicted of the felony.

"totally" is definitely the wrong word to use to intensify the adjective.

I don't understand your phrase "the first man of the court" but it might be a stylistic choice on your part, so there's no need to change it (i.e. the grammar is fine but the style is strange).

A little note about court vocabulary: if the accused has been found guilty he has also been convicted of the crime. It doesn't make sense to say that he was convicted only after the judge started speaking because the jury has already convicted him.

The judge sentenced him to 10 years in prison, athough the guilty man was hoping to be acquintted of the punishment.

You don't need the phrase "of the punishment" since he can't be acquitted of anything else.

After he went to jail, he was released, h. He served only 5 years, because he ended up getting time off for good behaviour.

Just a small problem of tense.

I am totally convinced that it is quite hard to make a decision in a case like that.

"totally" is not a good word to use so regularly. It makes you sound like an American teenager. If you want to sound American teenager, by all means use it freely. However, I assume you wouldn't want that and I've corrected it as such.

I am noteither for nor against long prison sentences, because I do not have enough information about the topic and I have never learnstudied law.

"neither... nor..." is the appropriate construction here, though what you had could work in colloquial English.

To say you don't "have information" about a topic is to say that you know absolutely nothing about it at all, which is not the case here.