If there was a case registered against you and a fine was paid as a court order, then it is documented, and the record will remain. If it was just a fine issued on the street or at a station and only a receipt was produced, then it will not have a long-term record for background verifications.
The time frame would also be important. If the conviction was recent, then the police may remember it and create an issue for the verification certificate (if applicable for the type of visa).
Some countries have very strict verification checks for "resident visas"; for most other countries and business visas/short visit visas, the process would be more lenient.
On a slightly different note, it is unfortunate that educated people like us tend to ignore the basic rules of life (whether it is a law or not) until they affect a life-changing decision. All readers of this blog should take this example to understand that even small mistakes can make you vulnerable at the most crucial point in life; hence, we should all be vigilant to avoid such mistakes.
Best Regards,
Amod Bobade