A Patna fast track on Saturday sentenced three persons to life sentence in connection with NHAI engineer Satyendra Dubey murder case.
Additional district judge of fast track court-V pronounced the verdict. Senior CBI lawyer L R Ansari told The Indian Express: "As it was not rarest of rare case with murder with intention of robbery, both prosecution and defence pleaded the court of punishment deemed fit in the case by the court".
All the three accused - currently lodged in Beur jail, were taken to court in police van. Mother of one of the accused Mantu was seen crying on sitting on court stairs after the verdict.
Dubey's family, however, stayed away from the court saying they had "little interest in the case as no big fishes getting caught by CBI". Satyendra Dubey's brother Dhananjay Dubey said: "Only small fries have got sentence".

Source : http://www.indianexpress.com/news/3sentencedtolifeinsatyendradubeymurdercase/596419 /

Please explain to me the emboldened parts.
Though I guess "court of punishments" means "legal punishment or punishment that is given by court".
I think "fast track" applies to this excerpt. It's not an example of careful grammar. It leans toward the chat room.

Both sides are asking the court to use its own discretion.

I take "not rarest of rare case" as sarcasm for "this is very common."
Nobody cares. The big fish always get away.
Students: Are you brave enough to let our tutors analyse your pronunciation?
Thank you Avangi for all your useful replies.

But I wonder what you mean by "fast track applies to the excerpt" though I know "excerpt" is a short piece of writing taken from other main sources.

Also I think you forgot to explain to me about "court of punishment" which I was desperately looking for.
The author of this "court report" of the proceedings in this case seemed to be in a real hurry. I find this "English" very hard to parse. Perhaps it is easily understood by some particular regional group.
I assumed your "example" was an excerpt from a longer news article. I may have been wrong.

I did not take "court of punishment" as a collocation. I don't think as a specific group of words it means anything.
Both the prosecution and the defence pleaded [that] the court (the fast track judge) use his own discretion in sentencing the accused. They pleaded the court for appropriate punishment. I may be wrong. I admit it doesn't make a whole lot of sense.

Have you tried Googling "court of punishment"?

Edit. Okay, I'm wrong. "Court of punishment" is an expression describing a court which gives out punishment, as opposed to one which merely settles issues, I guess like a civil court or family court or divorce court. There was a reference from the state of Michigan in the US.
Sorry about that! I had never heard the expression before.