Is there a canon statement or quote from J.K. Rowling that says that Voldemort won or was a champion in the Tri-Wizard tournament when he was in Hogwarts? If there is why didn't J.K. Rowling mention that about Tom Riddle's time in Hogwarts like she mentioned he was a prefect and the head boy? If not why didn't he join the tournament?
It is not possible at all that Voldemort would have taken part in that tournament as it was not held for over 200 years (since 1792 to be exact). I have no english version of the books on hand, but on Pottermore you can read the following text:
after some, err, accidents, (all three champions were injured in 1792) the contest petered out. That was until its revival two centuries later in 1994, when extra safety precautions were added by the organisers.
Per Harry Potter and the Goblet of Fire.
‘As I was saying,’ he said, smiling at the sea of students before him, all of whom were still gazing transfixed at Mad-Eye Moody, ‘we are to have the honour of hosting a very exciting event over the coming months, an event which has not been held for over a century. It is my very great pleasure to inform you that the Triwizard Tournament will be taking place at Hogwarts this year.’
HP:GoF - Chapter 12: The Triwizard Cup
Since Voldemort is only in his 70s at the point at which he dies (indicating that he was likely born in the late 1920s) and the last Triwizard cup was held some time before the late 1800s, Voldemort can't possibly have taken part* in a Triwizard cup since the last one was held at least 50 years before he was at Hogwarts.
*Unless he used a time-turner, obvs
It has since been revealed on Pottermore that the Tournament was formally cancelled in the 1790's however, Dumbledore does note that there have been attempts at revivals since that point.
‘There have been several attempts over the centuries to reinstate the Tournament,’ Dumbledore continued, ‘none of which have been very successful.
According to Pottermore, the Triwizard Tournament was discontinued mid-18th century and only resumed during Harry's 4th year. Thus, Tom Riddle couldn't have participated in it.